EXST 2201 Exam 2

What type of information do we really wish the science of statistics would give us so that we could make a good decision about an important matter? (4.1)

a. Information about probability.

b. Information about the population.

c. Information about the sample.

d. Information about descriptive statistics.

b. Information about the population.

Why does a column of population data values contain more information about the population than a column of sample data values? (4.1)

a. Because the population data values are used to get the sample data values.

b. Because populations are defined by the researcher, so they inherently have more information.

c. Because the population is the totality of the individuals of interest.

d. A column of population data values has more data values than a column of sample data values.

d. A column of population data values has more data values than a column of sample data values.

What are statistical methods of inference used for? (4.1)

a. To get information about population data values.

b. To infer an appropriate statistical result.

c. To go from a known situation to an unknown situation.

d. To infer information about descriptive statistics.

a. To get information about population data values.

Which one of the following choices does NOT indicate why knowing the value of the population mean is so important in the science of statistics? (4.1)

a. Because the population mean was one of the first statistical methods developed.

b. Because one value describing a population is much easier to work with than many values.

c. Because it is a critical parameter of the normal distribution.

d. Because it reduces a column of data values down to the one most representative value.

a. Because the population mean was one of the first statistical methods developed.

In regard to normally distributed data values themselves, what is the importance of knowing the value of the population mean in the science of statistics? (4.1)

a. Most of the data values are clustered close to the value of the mean.

b. The mean summarizes the location information of the data values.

c. The mean is required to find probability with the normal distribution.

d. The mean gives the mathematical first moment of the data values.

a. Most of the data values are clustered close to the value of the mean.

In the common, real-world practice of statistics, is it ever possible to know the true value of the population mean? (4.1)

a. No, because populations are usually hypothetical and their information cannot be known.

b. All these other choices.

c. No, because we cannot do calculations on an infinite number of data values.

d. No, because the science of statistics deals with probabilistic data.

b. All these other choices.

Why is the sample average important in the science of statistics? (4.1)

a. It is easy to use being one value summarized from the data values.

b. It is the middle of the sample data values.

c. It best estimates the value of the population mean from the sample data values.

d. It used the same mathematical calculation as the population mean.

c. It best estimates the value of the population mean from the sample data values.

Please match each type of statistical method below with the name of the appropriate statistical method. (4.1)

1- Estimate the population mean.

2- Test for the population mean.

A- Hypothesis testing

B- Confidence Intervals

Estimate the population mean. : Confidence Intervals

Test for the population mean. : Hypothesis Testing

What is the end result of the confidence interval method? (4.1)

a. A resulting value for the population mean.

b. A conclusion to a statistical test about a population mean.

c. A level of confidence in the value of the population mean.

d. An interval estimate of the population mean.

d. An interval estimate of the population mean.

What is the end result of the hypothesis test method? (4.1)

a. A conclusion to a statistical test about a population mean.

b. An interval estimate of the population mean.

c. A resulting value for the population mean.

d. A level of confidence in the value of the population mean.

a. A conclusion to a statistical test about a population mean.

Please match each step in the General Method for Solving Problems in Statistics below with its purpose. (4.1)

1- Step A

2- Step 1

3- Step 2

4- Step 3

A. Theorize probability information.

B. Abstract problem information.

C. Infer population information.

D. Analyze sample information.

Step A: Abstract problem information.

Step 1: Theorize probability information.

Step 2: Analyze sample information.

Step 3: Infer population information.

Choose the two parts of Step A: Abstract below? (4.1)

a. Write the two hypotheses.

b. Find the critical value.

c. Get descriptive statistics.

d. Calculate the test statistic.

a. Write the two hypotheses.

c. Get descriptive statistics.

Choose the two tools used in Step 1: Theorize below?(4.1)

a. The Schematic z-Curve.

b. The z-Table.

c. The Probability Calculator.

d. The Equation for sample average

a. The Schematic z-Curve.

b. The z-Table.

What is the primary task in Step 2: Analyze? (4.1)

a. Pick the appropriate Schematic Curve.

b. Start the process of statistical inference.

c. Analyze the problem for what it is asking.

d. Choose the appropriate equation.

d. Choose the appropriate equation.

What is the end result of Step 3: Infer? (4.1)

a. The true value of the population mean.

b. A concise description of the column of sample data values.

c. A sample average estimating the value of a population mean.

d. Statistical information about the value of a population mean.

d. Statistical information about the value of a population mean.

Why does having more sample data values mean getting more information about the population data values? (4.1)

a. Because statistical methods are designed for an infinite number of data values.

b. Because each data value brings a bit more information about the population data values.

c. Because mathematical calculations are more efficient with more data values.

d. Because calculation error is less with more data values.

b. Because each data value brings a bit more information about the population data values.

What type of statistics are used to learn about sample data values? (4.1)

a. Descriptive statistics, because they describe the methods used on a column of sample data values.

b. Inferential statistics, because they use the information in a column of sample data values.

c. Descriptive statistics, because they describe the data values in a column of sample data values.

d. Inferential statistics, because sample data values come from population data values.

c. Descriptive statistics, because they describe the data values in a column of sample data values.

Please select the choice that is NOT a purpose of the Process of Abstraction? (4.1)

a. Choose the appropriate statistical method for the situation.

b. Summarize the question text into a reasonable size.

c. Convert real world information into statistical information.

d. Determine the proper equation to be used.

b. Summarize the question text into a reasonable size.

Abstract the situation below by matching the statistical symbols with their appropriate values?

An engineer was responsible for 5 machines making ball bearings 1.2 cm in diameter, with standard deviation of 0.01 cm. He suspected that one of the machines was making ball bearings too small, so he measured 37 ball bearings from this machine and found an average diameter of 1.15 cm. (4.1)

1-μ

2-σ

3-n

4-xbar

5-s

A. n/a

B. 0.01

C. 1.15

D. 1.2

E. 37

1-μ: 1.2

2-σ: 0.01

3-n: 37

4-xbar: 1.15

5-s: n/a

Abstract the situation below by matching the statistical symbols with their appropriate values?

Zillow lists the average home price in our area as $215,816 with a standard deviation of $21,500. To find out if this was still true, a real estate professional collected the data for 58 recently sold homes and found an average of $235,000 with a standard deviation of $23,500.(4.1)

1-μ

2-σ

3-n

4-xbar

5-s

A. 23,500

B. 215,816

C. 58

D. 21,500

E. 235,000

1-μ: 215,816

2-σ: 21,500

3-n: 58

4-xbar: 235,000

5-s: 23,500

The statement, 'On average, Americans spend around 4.5 hours per day on their phones.' has what interpretation in the process of abstraction?(4.1)

a. That the Americans studied spend 4.5 hours. (x)

b. That it is a generic statement giving information. (x)

c. That all Americans spend 4.5 hours.

d. That some Americans spend 4.5 hours.

c. That all Americans spend 4.5 hours.

What is the correct symbol for the significance level of a statistical study?(4.1)

a. Beta (β).

b. Significance Level (SL).

c. Alpha (α).

d. Chi-Square (χ2).

c. Alpha (α).

Abstract the situation below by matching the statistical symbols with their appropriate values?

A college student measured how long per day she studied for 14 days. She calculated an average of 5.3 hours per day and a standard deviation of 1.2 hours per day. Past studies have shown that college students study 4.1 hours each day with a standard deviation of 0.7 hours each day. (4.1)

1-μ

2-σ

3-n

4-xbar

5-s

A. 0.7

B.5.3

C. 1.2

D. 14

E. 4.1

1-μ: 4.1

2-σ: 0.7

3-n: 14

4-xbar: 5.3

5-s: 1.2

What two tools are used to go between the blanks on the Algebraic side of the Schematic Curve for Sample Averages? (4.1)

a. z-Equation: z= x−μ / σ.

b. The z-Table.

c. The x-Table.

d. z-Equation: z= xbar−μ / σ√n.

b. The z-Table.

For the Method to Use the Schematic Curve, match each step below with it function? (4.1)

1- Step 1

2- Step 2

3- Step 3

4- Step 4

A. Solve for the answer.

B. Load the problem.

C. Draw the schematic.

D. Calibrate the x-Axis.

Step 1: Draw the schematic.

Step 2: Calibrate the x-Axis.

Step 3: Load the problem.

Step 4: Solve for the answer

What actions occur in the Analyze step of the General Method to Solve Problems in Statistics? (4.1)

a. Inferring a population value from a sample value.

b. Converting real world information into statistical information.

c. Finding the appropriate t-value for the situation.

d. The calculations for the method are chosen and performed.

d. The calculations for the method are chosen and performed.

What actions occur in the Infer step of the General Method to Solve Problems in Statistics? (4.1)

a. Finding the appropriate z-score for the situation.

b. Simplifying the problem into statistical information.

c. Solving the chosen equation.

d. Determining a population value from a sample values.

d. Determining a population value from a sample values.

There are two types of estimators of the population mean, the point estimator and the interval estimator. Please match each of the following estimators with their appropriate statistical method.(5.1)

1- Point

2- Interval

A. Confidence Interval

B. Sample Average

1- Point: Sample Average

2- Interval: Confidence interval

Two common statistical estimators of the population mean are the sample average and the confidence interval. Which one of these statistics is more useful to give information about the value of a population mean? (5.1)

a. Both, as they both estimate the same value (the population mean).

b. Confidence interval, as it shows how far the mean might be from the average.

c. Sample average, as it is the best guessed value for the mean.

d. Confidence interval, as it is wider and has a greater chance of being correct.

b. Confidence interval, as it shows how far the mean might be from the average.

Why is the confidence interval method the best method to get an interval estimate of the population mean? (5.1)

a. It gives a wider estimate than the sample average.

b. All of the other answers.

c. It uses the most information from the distribution of the data values.

d. It has a higher level of confidence than other interval estimators.

c. It uses the most information from the distribution of the data values.

What is a major weakness in the method of a confidence interval? (5.1)

a. Values outside of the confidence interval are not likely values for the population mean.

b. A confidence interval does not give a degree of reasonableness for any value to be the population mean.

c. Confidence intervals can be changed just by changing the level of confidence.

d. A confidence interval can give more than one interval for the population mean.

b. A confidence interval does not give a degree of reasonableness for any value to be the population mean.

The logic of a confidence interval comes from reversing the logic of the sampling distribution of the sample average. Thus, the schematic curve for a confidence interval is centered over which statistic for location? (5.1)

a. Sample median (M).

b. Sample average (¯x).

c. Population mode (Mode).

d. Population mean (μ).

b. Sample average (¯x).

What is the name of the spread in a confidence interval? (5.1)

a. The standard error.

b. The standard deviation.

c. The margin of error.

d. The coefficient of variation.

c. The margin of error.

Select two choices below that make up the two parts of a margin of error in a confidence interval? (5.1)

- The level of predictiveness in the confidence interval method.

- The standard deviation of the data values.

- The standard error of the sample average.

- The level of confidence in the confidence interval method.

- The standard error of the sample average.

- The level of confidence in the confidence interval method.

Please match each of the following changes in the calculation of the margin of error with their effect on the width of a confidence interval. Note which answer goes with which input change (n,CL). (5.1)

1-Increase sample size.

2-Decrease sample size.

3-Increase level of confidence.

4-Decrease level of confidence.

A. Narrower (CL).

B. Narrower (n).

C. Wider (CL).

D. Wider (n).

1-Increase sample size: Narrower (n)

2-Decrease sample size: Wider (n)

3-Increase level of confidence: Wider (CL)

4-Decrease level of confidence: Narrower (CL)

The schematic curve for a confidence interval divides the curve into several regions. Which region will always contain the population mean? (5.1)

a. Confidence region.

b. Mean region.

c. Middle region.

d. Significance region.

a. Confidence region.

The size of the confidence region is given by the size of the confidence level. What is a simple meaning of the confidence level? (5.1)

a. How many times out of 100 the method will give a correct answer.

b. How confident to be that the confidence interval contains the value of the population mean.

c. How many times out of 100 the method was calculated correctly.

d. How many times out of 100 the method will give an incorrect answer.

a. How many times out of 100 the method will give a correct answer.

What points on the real number line separate the confidence region from the significance regions? (5.1)

a. The significance values.

b. The schematic values.

c. The critical values.

d. The confidence values.

c. The critical values.

What is the size of the significance region? (5.1)

a. Confidence level (CL).

b. Beta (β).

c. Significance level (SL).

d. Alpha (α).

d. Alpha (α).

Is it guaranteed that confidence interval method will give an interval containing the population mean every time? (5.1)

a. No, the method will give an incorrect interval alpha (α) percent of the time.

b. No, the correctness of the method is limited by the quality of the data input.

c. Yes, every confidence interval contains the population mean.

d. No, probabilistic data almost never gives a correct answer.

a. No, the method will give an incorrect interval alpha (α) percent of the time.

Please match each of the following statistics with how often they give the true value of the population mean. (5.1)

1- Sample average.

2- Confidence interval.

3- Sample standard deviation.

A. CL percent of the time.

B. Almost never.

C. Always never.

1-Sample average: Almost never.

2-Confidence interval: CL percent of the time.

3-Sample standard deviation: Always never.

Confidence intervals can be thought to be composed of two parts, a middle value and a spread value. Please match each of the following parts of a confidence interval with their appropriate statistics. (5.1)

1- Middle.

2- Spread.

A. The value of the sample average.

B. The value of the margin of error.

Middle: The value of the sample average.

Spread: The value of the margin of error.

In a confidence interval, what information does the confidence level give? (5.1)

a. The proportion of times the confidence interval should be trusted.

b. The proportion of times the population mean is correct.

c. The proportion of times the confidence interval includes the population mean.

d. The proportion of times the calculations are correct.

c. The proportion of times the confidence interval includes the population mean.

In the science of statistics, why is the method of confidence intervals needed to get information about the population mean? (5.1)

a. As the population mean cannot be determined exactly from probabilistic sample data values.

b. As a single value was not considered valid enough for the population mean.

c. As intervals were known to be valuable in mathematics so the same concept was applied in statistics.

d. As the population mean cannot be known exactly in this course.

a. As the population mean cannot be determined exactly from probabilistic sample data values.

The statistical logic for a confidence interval is based on reversing already known logic for another statistic. What is this other logic? (5.1)

a. The logic for the sampling distribution of the sample average.

b. The logic for the distribution of the population mean.

c. The logic for the level of confidence.

d. The logic for the distribution of the data.

a. The logic for the sampling distribution of the sample average.

Is the interval shown below properly denotated for a confidence interval? (5.1)

(115,97)

a. Yes, as this interval has a middle part and a spread part.

b. No, as the value of the sample average must be in the middle of the interval.

c. Yes, this is a proper denotation for a confidence interval.

d. No, values in the parentheses must go from lowest to highest.

d. No, values in the parentheses must go from lowest to highest.

Looking in a schematic curve from the point of view of probability, what type of situation is a confidence interval? (5.1)

a. A side area.

b. A middle body area.

c. A right (or left) tail area.

d. A right (or left) body area.

b. A middle body area.

The curve in a schematic curve can be centered over different values to give different information about the data values. Please match each value below with what information is given about the data values. (5.1)

1- The population mean.

2- The sample average.

A. A range of likely values for the sample average.

B.A range of likely values for the population mean.

1-The population mean: A range of likely values for the sample average.

2-The sample average: A range of likely values for the population mean.

The lower and upper confidence limits for a confidence interval can be seen in a schematic curve. The two confidence limits are just the x-values of a middle body area in a schematic curve. (5.1)

a. Sometimes true.

b. None of the other answers.

c. Never true.

d. True.

d. True.

What is the main strength of a confidence interval? (5.1)

a. Gives a level of confidence for the value of the population mean.

b. It is easy to calculate and to interpret its meaning.

c. Gives a range of likely values for the population mean.

d. Gives a range of unlikely values for the population mean.

c. Gives a range of likely values for the population mean.

What is the major weakness of a confidence interval? (5.1)

a. Some confidence intervals give practically impossible values.

b. Confidence intervals do not explicitly give the middle and the spread values.

c. Some confidence intervals are too wide to be useful.

d. Every value inside the interval is equally likely to be the population mean.

d. Every value inside the interval is equally likely to be the population mean.

What is the correct equation for a confidence interval with t-values? (5.1)

a. CI%=¯x±t(α/2,n−1)(s/√n)

b. CI%=μ±t(α/2,n−1)(s/√n)

c. CI%=¯x±t(α/2,n−1)(s/n)

d. CI%=¯x±t(α/2,n−1)(√s/n)

a. CI%=x¯±t(α/2,n−1)(s/√n)

Consider the size of the significance region, what is its appropriate symbol and how is it calculated? (5.1)

a. α=1+CL.

b. α=1−CL.

c. σ=CL−α.

d. β=CL−1.

b. α=1−CL.

Will every confidence interval contain the value of the population mean? (5.1)

a. No, only the confidence level proportion of the time.

b. No, as the population mean is either inside or outside the confidence interval.

c. No, but it will most of the time.

d. Yes, unless the calculations are done incorrectly.

a. No, only the confidence level proportion of the time.

What is the critical value for a 95% confidence interval with 22 data values and the sample standard deviation? (5.1)

a. Critical value = 2.080.

b. Critical value = 1.721.

c. Critical value = 1.960.

d. Critical value = 2.074.

a. Critical value = 2.080.

What is the critical value for a 90% confidence interval with 31 data values and the sample standard deviation? (5.1)

a. Critical value = 1.697.

b. Critical value = 1.696.

c. Critical value = 1.640.

d. Critical value = 1.310.

a. Critical value = 1.697.

What is the critical value for a 99% confidence interval with 10 data values and the sample standard deviation? (5.1)

a. Critical value = 3.250.

b. Critical value = 3.169.

c. Critical value = 2.821.

d. Critical value = 2.764.

a. Critical value = 3.250.

In the confidence interval equation shown below, what part of the equation is the margin of error? (5.1)

CI%=¯x±t(α/2,n−1)(s√n)

a. ME=(s/√n)

b. ME=t(α/2,n−1)

c. ME=¯x±(s/√n)

d. ME=t(α/2,n−1)(s/√n)

d. ME=t(α/2,n−1)(s/√n)

If the degrees of freedom gives the number of units of information, what does the margin of error give? (5.1)

a. Half the width of a confidence interval.

b. The entire width of a confidence interval.

c. Half the size of the significance region.

d. The level of confidence in the confidence interval.

a. Half the width of a confidence interval.

When the confidence level is increased, how does the width of the confidence interval change? (5.1)

a. Widens, as the middle body area gets larger.

b. Narrows, as there is more information in the confidence interval.

c. Narrows, as there is more confidence in the method.

d. Widens, as the tail areas get larger.

a. Widens, as the middle body area gets larger.

When the number of data values is increased, how does the width of the confidence interval change? (5.1)

a. Narrows, as the standard error of the sample average gets smaller.

b. Narrows, as the degrees of freedom get larger.

c. Widens, as the calculations increase in size.

d. Widens, as more data values mean more information.

a. Narrows, as the standard error of the sample average gets smaller.

Two pieces of information must be known to use the t-distribution to find the probability of an event. What are those two pieces of information? (5.3)

a. Sample average / Number of data values.

b. Sample standard deviation / Sample average.

c. Population standard deviation / Number of data values.

d. Sample standard deviation / Degrees of freedom.

d. Sample standard deviation / Degrees of freedom.

What is the value of the sample average / value of the margin of error in the confidence interval shown below? (5.3)

(96, 118)

a. Values = 108 / 13.

b. Unknown from this information / Unknown from this information.

c. Values = 107 / 22.

d. Values = 107 / 11.

d. Values = 107 / 11.

Is the following a true statement? 'A confidence interval is used to infer the value of the sample average'. (5.3)

a. Yes, as the sample average is a random variable.

b. No, as it is used to find the value of the population mean.

c. No, as it is used to find the value of the population standard deviation.

d. Yes, as the population mean can never be really known.

b. No, as it is used to find the value of the population mean.

Is the following a true statement? 'The population mean must be known to calculate a confidence interval'. (5.3)

a. Yes, as the population mean is needed to find probability from a schematic curve.

b. No, as the sample average can be used to estimate the value of the population mean.

c. Yes, as the equations are designed to use the population mean.

d. No, as finding the value of the population mean is the goal.

d. No, as finding the value of the population mean is the goal.

What is the meaning of the values inside a properly made confidence interval? (5.3)

a. The middle values are likeliest to be a value for the population mean.

b. Any of these values could be a likely value for the population mean.

c. None of these values could be a likely value for the population mean.

d. These values are the point estimates for the value of the population mean.

b. Any of these values could be a likely value for the population mean.

A local college instructor gave a statistics exam to his class of 31 students and calculated a 95% confidence interval of (77.1, 82.9) for the scores. A competing college knew that their students scored an average of 85 on this same test. How well did the local college do in comparison to the competing college? (5.3)

a. Not well, as a sample average score of 85 is higher than a sample average score of 80.

b. Not well, as 85 is higher than the upper confidence limit.

c. Cannot answer this question with this information.

d. Very well, as 85 is not inside the confidence interval.

b. Not well, as 85 is higher than the upper confidence limit.

31 students in a local statistics class took an exam where the average score was 80, and the standard deviation score was 10. Students in a competing statistics class took the same exam and had an average score of 85. Did the competing students score higher than the population mean of the local students? Make a 95% confidence interval to find out. (5.3)

a. Yes, as CI = (79.3, 80.6).

b. Yes, as CI = (76.3, 83.7).

c. Yes, as CI = (76.5, 83.5).

d. Yes, as CI = (77.0, 83.0).

b. Yes, as CI = (76.3, 83.7).

The ages of 21 people in an elder care home had an average age of 85 years and a standard deviation age of 8 years. Could the population mean age of people in an elder care home be 87 years? Make a 90% confidence interval to find out. (5.3)

a. Yes, as 87 is inside of CI = (80.358, 89.642).

b. Yes, as 87 is inside of CI = (81.989, 88.011).

c. No, as 87 is outside of CI = (84.495, 85.505).

d. Yes, as 87 is inside of CI = (82.687, 87.313).

b. Yes, as 87 is inside of CI = (81.989, 88.011).

In 2015 on the National Assessment of Educational Progress (NAEP) science scale, the following results were obtained.

Score for 15 underage students: average = 125, standard deviation = 5.81.

Score for 15 over age students: average = 136, standard deviation = 3.87.

Both data shapes were normal. Please make two 98% confidence intervals to find out if it is reasonable that these two groups of students have the same population mean score. (5.3)

a. No, as the two confidence intervals, (124.0, 126.0) and (135.3, 136.7) do not overlap

b. No, as the two confidence intervals, (121.1, 128.9) and (133.4, 138.6) do not overlap.

c. Yes, as the two confidence intervals, (109.8, 140.2) and (125.8, 146.2) do overlap

d. No, as the two confidence intervals, (121.6, 128.3) and (133.7, 138.2) do not overlap

b. No, as the two confidence intervals, (121.1, 128.9) and (133.4, 138.6) do not overlap.

An auto mechanic wants to estimate the cost of repairing a car after a 25 mph collision. He looked up 24 collisions and found that the average repair cost was $11,000 with a standard deviation cost of $2,500. Please find the middle value / spread value of a 98% confidence interval for the population mean repair cost. ? (5.3)

a. Values = $11,000 / $1,778.

b. Values = $11,000 / $673.

c. Values = $11,000 / $1,111.

d. Values = $11,000 / $1,276.

d. Values = $11,000 / $1,276.

Last year a sample of 35 women who were victims of purse snatching had an average age of 34.25 years, with a standard deviation age of 10 years. One researcher wondered if the population mean age of all victims of purse snatching could be less than 30 years. Make a 96% confidence interval to find out? (5.3)

a. No, as the confidence interval for age = (31.15, 37.35)

b. No, as the confidence interval for age = (33.64, 34.86)

c. No, as the confidence interval for age = (30.64, 37.86).

d. Yes, as the confidence interval for age = (29.38, 39.12)

c. No, as the confidence interval for age = (30.64, 37.86).

The height of 14 students in a college statistics course was measured and found to have an average height of 68 inches, and a standard deviation height of 2 inches. What is the 90% confidence interval for the mean height of all students at the college? (5.3)

a. CI = (67.3, 68.7)

b. CI = (66.9, 69.0)

c. CI = (67.0, 68.9).

d. CI = (67.7, 68.2)

c. CI = (67.0, 68.9).

The height of 27 students in a college statistics course was measured and found to have a 90% confidence interval height of (65.9, 69.9). Is it possible that the mean height of all the students at this college 5 feet 6 inches (66 inches) or higher? (5.3)

a. Yes, as 66 inches is inside the confidence interval.

b. No, as 66 inches is not in the middle of the confidence interval.

c. Yes, as most of the confidence interval is greater than 66 inches.

d. Yes, as 66 inches is below the value of the sample average.

a. Yes, as 66 inches is inside the confidence interval.

The confidence interval shown below was calculated from a sample average of 100 and a margin of error of 15. Is 100 a more likely value for the population mean than 90? (5.3)

(85, 115)

a. No, as all values inside the confidence interval are equally likely.

b. Yes, as 100 is closer to the middle of the confidence interval.

c. Maybe, it depends on the degrees of freedom and the t-value.

d. Yes, at the sample average is the best point estimator of the population mean.

a. No, as all values inside the confidence interval are equally likely.

A fishery graduate student wanted to know the population mean length of perch in a local lake. She caught 10 perch, measured their length, and found an average length of 3.6 inches, and a standard error of the sample average length of 0.994 inches. What is the 95% confidence interval for the population mean length of the perch in this lake? (5.3)

a. CI = (1.35, 5.85)

b. CI = (2.89, 4.31)

c. CI = (3.50, 3.70)

d. CI= (1.78, 5.42)

a. CI = (1.35, 5.85)

A fishery graduate student wanted to know the population mean length of perch in a local lake. She caught all the perch she could and claimed that this was all the perch in the lake. Since she claimed that she had caught the population, she chose to use the z-distribution to calculate a confidence interval for the value of the population mean. What do you think of her choice of distribution? (5.3)

a. Incorrect, if she did catch the entire population of perch, then why estimate the population mean.x

b. Incorrect, how could she be certain that she had caught the entire population.

c. All of these other answers.

d. Incorrect, as the proper form of the standard deviation would not be known.

c. All of these other answers.

38 eggs were randomly chosen from a grocery store and individually weighed. The average weight was 97.8 grams with a standard deviation weight of 4.2 grams. What is the standard error of the sample average / margin of error for a 90% confidence interval for weight? (5.3)

a. Grams = 0.6813 / 1.1494

b. Grams = 0.1105 / 0.1865

c. Grams = 0.6813 / 0.8891

d. Grams = 4.2000 / 7.0854

a. Grams = 0.6813 / 1.1494

A researcher was interested in the proportion of the population that was left-handed. He collected 61 random samples of 100 people each and found that an average of 16 people were left-handed, with a standard deviation of 4 people. What is the 95% confidence interval for the population mean number of left-handed people in a sample of 100 people? (5.3)

a. CI = (15.00, 17.00)

b. CI = (15.87, 16.94)

c. CI = (14.97, 17.02).

d. CI = (14.88, 17.12)

c. CI = (14.97, 17.02).

Click two of the following choices as the reasons why the method of hypothesis testing is needed. (6.1)

-To answer if the null value is less than, or greater than, the population mean.

-To learn the reasonableness that the null value is the value of the population mean.

-To determine if the alternate hypothesis is appropriate for this statistical situation.

-To determine if the null hypothesis is appropriate for this statistical situation.

-To learn the reasonableness that the null value is the value of the population mean.

-To answer if the null value is less than, or greater than, the population mean.

In the statistical method of hypothesis testing, what is the meaning of the word reasonableness? (6.1)

a. How reasonable is the conclusion of the hypothesis test.

b. How close is the null value to the value of the population mean.

c. How reasonable is the null value the value of the population mean.

d. How reasonable is the null hypothesis for this statistical situation.

c. How reasonable is the null value the value of the population mean.

In the alternative hypothesis of a hypothesis test, what is the meaning of the words 'less than', or 'greater than'? (6.1)

a. Could the value in the null hypothesis be equal to the value of the population mean.

b. Could the value in the null hypothesis be both less than, or greater than, the value of the population mean.

c. Could the value of the population mean be less than, or greater than, the value in the null hypothesis.

d. Could the value of the sample average be less than, or greater than, the value in the null hypothesis.

c. Could the value of the population mean be less than, or greater than, the value in the null hypothesis.

In the statistical method of hypothesis testing, choose two of the choices below as the assumptions required to perform a hypothesis test. (6.1)

-The data values are normally distributed.

-The individuals were randomly selected.

-The sample average is normally distributed.

-The sample size is greater than 30 data values

-The individuals were randomly selected.

-The sample average is normally distributed.

For the General Method to solve problems in statistics, please match each step with the type of information that step works with. (6.1)

1-A: Abstract.

2-1: Theorize.

3-2: Analyze.

4-3: Infer.

A.Sample info from problem.

B.Probability info from theory.

C.Relevant info from problem.

D.Population info as a result.

A: Abstract- Relevant info from problem.

1: Theorize- Probability info from theory.

2: Analyze- Sample info from problem.

3: Infer- Population info as a result.

In the statistical method of hypothesis testing, which of the choices below is NOT a descriptive statistic. (6.1)

a. Statistic = ¯x.

b. Statistic = t0.

c. Statistic = n.

d. Statistic = s.

b. Statistic = t0.

In the statistical method of hypothesis testing, what belief about the population mean does the null hypothesis (H0) express? (6.1)

a. The currently believed value of the population mean.

b. The mathematical value of the population mean.

c. The researcher's believed value of the population mean.

d. The preferred value of the population mean.

a. The currently believed value of the population mean.

In the statistical method of hypothesis testing, what belief about the population mean does the alternative hypothesis (H1) express?

What information does the alternative hypothesis express? (6.1)

a. The researcher's believed value of the population mean.

b. The currently believed value of the population mean.

c. The mathematical value of the population mean.

d. The preferred value of the population mean.

a. The researcher's believed value of the population mean.

In the statistical method of hypothesis testing, please match each region below with the appropriate area under a schematic normal curve. (6.1)

1-Acceptance Region.

2-Less than Rejection Region.

3-Greater than Rejection Region.

4-Not-Equal-To Rejection Region.

A. A two-tail area.

B. A right-tail area.

C. A middle body area.

D. A left-tail area.

1-Acceptance Region: A middle body area.

2-Less than Rejection Region: A left-tail area.

3-Greater than Rejection Region: A right-tail area.

4-Not-Equal-To Rejection Region: A two-tail area.

In the statistical method of hypothesis testing, for the value that separates the schematic curve into the acceptance region and the rejection region(s), what is its name / where does it come from? (6.1)

a. The test statistic / From the z,t-Equation.

b. The critical value / From the z,t-Table.

c. The p-value / From the z,t-Table.

d. The p-value / From the z,t-Equation.

b. The critical value / From the z,t-Table.

In the statistical method of hypothesis testing, where does the value of the test statistic come from? (6.1)

a. From the t-table (t0=2.359).

b. From the value in the null hypothesis.

c. From the z-equation (z0=x−μ/s).

d. From the t-equation (t0=¯x−μ/s/√n).

d. From the t-equation (t0=¯x−μ/s/√n).

In the statistical method of hypothesis testing, p-value gives the size of which area(s) in a schematic curve? (6.1)

a. The middle body area from the value of the population mean.

b. The tail area(s) from the value of the sample average.

c. The tail area(s) from the value of the test statistic.

d. The tail area(s) from the value of the critical value.

c. The tail area(s) from the value of the test statistic.

In the statistical method of hypothesis testing, what happens to the Type-II Error when the Type-I Error is decreased? (6.1)

a. There is no relationship between the Type-I and Type-II Errors.

b. The Type-II Error does not change.

c. The Type-II Error decreases.

d. The Type-II Error increases.

d. The Type-II Error increases.

In the science of statistics, why is the method of hypothesis testing called an inferential method of statistics? (6.1)

a. It infers the best guess of the value of the population mean from the sample information.

b. It infers whether the researcher's belief is correct from sample information. x

c. It was created on purpose to be an inferential method in statistics.

d. It uses similar mathematics to a confidence interval, which is an inferential method.

a. It infers the best guess of the value of the population mean from the sample information.

In the statistical method of hypothesis testing, how is an inference about a population mean actually made? (6.1)

a. By checking if the critical value is inside the confidence interval.

b. By finding out if the value of the test statistic is less than zero.

c. By seeing if the test statistic lies in the critical region. x

d. By determining if the test statistic is close or far from the null value.

d. By determining if the test statistic is close or far from the null value.

In the statistical method of hypothesis testing, what value determines if the test statistic is close or far / where does it come from? (6.1)

a. The critical value / from the z,t-table.

b. The test statistic value / from the z,t-equation.

c. The significance value / from the researcher.

d. The null value / from the null hypothesis.

a. The critical value / from the z,t-table.

In the statistical method of hypothesis testing, how is the distance between the test statistic and the null value determined? (6.1)

a. By converting into z,t-values and finding the mathematical distance.

b. By converting into z,t-values and comparing on a real number line.

c. By converting into z,t-values and finding the statistical distance.

d. By converting into z,t-values and comparing on a t-Table.

c. By converting into z,t-values and finding the statistical distance.

In the statistical method of hypothesis testing, please match each question of interest below with what value the schematic curve is centered over, (6.1)

1- Probability.

2- Confidence Interval.

3- Hypothesis Test.

A. The population mean.

B. The null value.

C. The sample average.

1- Probability: The population mean.

2- Confidence Interval: The sample average.

3- Hypothesis Test: The null value.

In the statistical method of hypothesis testing, please select two choices that are the parts of Step A: Abstract. (6.1)

- Find the critical value from probability.

- Calculate the test statistic from the sample information.

- Get descriptive statistics from the sample data values.

- Write the researcher's question into two hypotheses.

- Get descriptive statistics from the sample data values.

- Write the researcher's question into two hypotheses.

In the statistical method of hypothesis testing, where does the null value NOT come from? (6.1)

a. From results from the sample.

b. All these other answers.

c. From the results of prior research.

d. From an expert in the field of study.

a. From results from the sample.

In the statistical method of hypothesis testing, please match each mathematical sign in a hypothesis to its situation in a distribution. (6.1)

1- Less than sign (μ≤0).

2- Greater than sign (μ≥0).

3- Not equal sign (μ≠0).

4- Equal sign (μ=0).

A. A right-tail situation.

B. A left-tail situation.

C. A null hypothesis.

D. A two-tail situation.

1-Less than sign (μ≤0): A left-tail situation.

2-Greater than sign (μ≥0): A right-tail situation.

3-Not equal sign (μ≠0): A two-tail situation.

4-Equal sign (μ=0): A null hypothesis.