EXST 2201 Exam 2

Information about the population.

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?

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

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

To get information about population data values.

What are statistical methods of inference used for?

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

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?

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

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

All these other choices.

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

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

Why is the sample average important in the science of statistics?

Estimate the population mean - confidence intervals

Test for the population mean - hypothesis testing

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

1. A.  Confidence Intervals

2. B.  Hypothesis Testing

Estimate the population mean.

Test for the population mean.

An interval estimate of the population mean.

What is the end result of the confidence interval method?

A conclusion to a statistical test about a population mean.

What is the end result of the hypothesis test method?

Step A: Abstract problem information

Step 1: Theorize propability information

Step 2: Analyze sample information

Step 3: Infer population information

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

1. A.  Abstract problem information.

2. B.  Analyze sample information.

3. C.  Infer population information.

4. D.  Theorize probability information.

Step A:

Step 1:

Step 2:

Step 3:

1. Write the two hypotheses

2. Get descriptive statistics

Choose the two parts of Step A: Abstract below?

1. The z-table

2. The Schematic z-Curve

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

Choose the appropriate equation.

What is the primary task in Step 2: Analyze?

Statistical information about the value of a population mean.

What is the end result of Step 3: Infer?

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

Why does having more sample data calues mean getting more information about the population data values?

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

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

Summarize the question text into a reasonable size.

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

1.μ - 0.5

2. σ,s - n/a

3. n - 25

4. ¯x - 0.55

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

 

A veterinarian wanted to know if the average weight of puppies born in her clinic was than 0.5 pounds. She weighed 25 puppies and found a sample average weight of 0.55 pounds.

A.  

0.5

B.  

25

C.  

n/a

D.  

0.55

1. μ

2. σ,s

3. n

4. ¯x

1. μ - 1.2

2. σ - 0.01

3. n - 37

4. ¯x - 1.15

5. s - n/a

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.

A.  

0.01

B.  1.2

C.  37

D.  1.15

E.  

n/a

1. μ

2. σ

3. n

4. ¯x

5. s

1. μ - 215,816

2. σ - 21,500

3. n - 58

4. ¯x - 235,000

5. s - 23,500

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.

A.  215,816

B.  58

C.  235,000

D.  23,500

E.  21,500

1. μ

2. σ

3. n

4. ¯x

5. s

1. μ,σ - n/a

2. n - 3,412

3. ¯x - 1.7

4. s - 0.7

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

 

A brand new researcher was studying mosquitos in Louisiana. He collected 3,412 mosquitos and found an average weight of 1.7 grams with a standard deviation of 0.7 grams. Now he would like to do a statistical analysis to find out what the data values tell him.

A.  

n/a

B.  

3,412

C.  

1.7

D.  

0.7

1. μ,σ

2. n

3. ¯x

4. s

That all Americans spend 4.5 hours.

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

Alpha (α)

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

1. μ - 23

2. σ - 3.7

3. n,¯x,s - n/a

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

 

Ford trucks get an average of 23 miles per gallon (mpg), with a standard deviation of 3.7 mpg.

A.  

23

B.  

n/a

C.  

3.7

1. μ

2. σ

3. n,¯x,s

1. μ - 14

2. n,σ,s - n/a

3. ¯x - 12

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

 

It is known that inshore fishermen catch 14 fish per trip in the nearby waters. A visiting fisherman recently made several trips in the nearby waters and caught an average of only 12 fish.

A.  

12

B.  

14

C.  

n/a

1. μ

2. n,σ,s

3. ¯x

1. μ - 4.1

2. σ - 0.7

3. n - 14

4. ¯x - 5.3

5. s - 1.2

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.

A.  14

B.  1.2

C.  0.7

D.  

5.3

E.  4.1

1. μ

2. σ

3. n

4. ¯x

5. s

1. μ,σ - n/a

2. n1 - 30

3. n2 - 25

4. ¯x1 - 78%

5. ¯x2 - 83%

6. s1 - 10%

7. s2 - 13%

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

 

At a local university, education researchers wanted to find out how students taught in on-campus math courses compared to students taught in a local Mathnasium franchise.

• Group 1: Thirty (30) students were randomly selected and assigned to an on-campus course

• Group 2: Twenty-five (25) students were randomly selected and assigned to Mathnasium courses.

At the end of the semester, each student took a standardized exam in mathematics. The scores had a normal shape. The students in Group 1, the on-campus course, had an average score of 78 with a standard deviation of 10. The students in Group 2, the Mathnasium course, had an average score of 83 with a standard deviation of 13.

A.  

78%

B.  

30

C.  

10%

D.  

83%

E.  

25

F.  

13%

G.  

n/a

1. μ,σ

2. n1

3. n2

4. ¯x1

5. ¯x2

6. s1

7. s2

1. μ - 17

2. σ - 10.5

3. n,¯x,s - n/a

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

 

A college undergraduate student in psychology was interested in the cognitive effects of high school students watching movies on a cell phone. To plan his study, he scanned the current literature to learn what was known at this time. He found that high school students watched movies for an average of 17 hours, with a standard deviation of 10.5 hours.

A.  

17

B.  

n/a

C.  

10.5

1. μ

2. σ

3. n,¯x,s

1. The z-Table

2. This z-Equation:  z=¯x−μ/σ√n.

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

Step 1 - Load the problem

Step 2 - Calibrate the x-axis

Step 3 - Draw the schematic

Step 4 - Solve for the answer

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

A.  Load the problem.

B.  Solve for the answer.

C.  

Calibrate the x-Axis.

D.  Draw the schematic.

Step 1.

Step 2.

Step 3.

Step 4.

The calculations for the method are chosen and performed.

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

Determining a population value from a sample values.

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

1. Point - sample average

2. Interval - confidence interval

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.

A.  

Confidence Interval

B.  

Sample Average

1. Point

2. Interval.

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

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?

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

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

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

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

Sample average (¯x)

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?

The margin of error.

What is the name of the spread in a confidence interval?

1. The level of confidence in the confidence interval method.

2. The standard error of the sample average.

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

1. C - Narrower (n).

2. D - Wider (n).

3. B - Wider (CL).

4. A - Narrower (CL).

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).

A.  

Narrower (CL).

B.  

Wider (CL).

C.  

Narrower (n).

D.  

Wider (n).

1. Increase sample size.

2. Decrease sample size.

3. Increase level of confidence.

4. Decrease level of confidence.

Confidence region

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

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

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

The critical values.

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

Alpha (α).

What is the size of the significance region?

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

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

1. Almost never

2. CL percent of the time

3. Always never

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

A.  

Always never.

B.  

Almost never.

C.  

CL percent of the time.

1. Sample average.

2. Confidence interval.

3. Sample standard deviation.

1. The value of the sample average.

2. The value of the margin of error.

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.

A.  

The value of the margin of error.

B.  

The value of the sample average.

1. Middle.

2. Spread.

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

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

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

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

The logic for the sampling distribution of the sample average.

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

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

Is the interval shown below properly denoted for a confidence interval? (115, 97)

A middle body area.

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

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

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

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.

A.  

A range of likely values for the sample average.

B.  

A range of likely values for the population mean.

1. The population mean.

2. The sample average.

True.

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.

Gives a range of likely values for the population mean.

What is the main strength of a confidence interval?

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

What is the major weakness of a confidence interval?

CI%=¯x±t(α/2,n−1)(s√n)

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

α=1−CL.

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

No, only the confidence level proportion of the time.

Will every confidence interval contain the value of the population mean>

Critical value = 2.080.

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

Critical value = 1.697.

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

Critical value = 3.250.

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

ME=t(α/2,n−1)(s√n)

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

Half of the width of a confidence interval.

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

Widens, as the middle body area gets larger.

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

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

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

Sample standard deviation/Degrees of freedom.

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?

Values = 107/11

What is the value of the sample average/value of the margin of error in the confidence interval shown below? (96, 118)

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

Is the following a true statement? ‘A confidence interval is used to infer the value of the sample average.’

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

Is the following a true statement? ‘The population mean must be known to calculate a confidence interval.’

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

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

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

A local college instructor gave a statistics exam to his class of 31 students and calculated a 95% confidence intercal 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?

Yes, as CI = (76.3, 83.7)

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.

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

The ages of 21 people in an elder care home had an average age of 85 years and a standard devaition 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.

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

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.

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

An auto mechanic wants to estimae the cost of repairing a car after a 25mph 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?

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

Last year a sample of 35 women who were victims of purse snatching had an average of 34.25 years, with a standard deviation 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?

CI = (67.0, 68.9)

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?

Yes, as 66 inches is inside the confidence interval.

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?

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

The confidence interval shown below was calculated from a sample average of 100 and a margin of error of 15. Is 100 a more liley value for the population mean than 90? (85, 115)

CI = (1.35, 5.85)

A fishery graduate student wanted to know the population mean length of a 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?

All of these other answers.

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?

Grams = 0.6813/1.1494

38 eggs were randomyl 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?

CI = (14.97, 17.02)

A researcher was interested in the proportion of the populationi 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?

1. To learns the reasonableness that the null value is the value of the population mean.

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

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

How reasonable is the null value of the population mean.

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

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

In the alternative hypothesis test, what is the meaning of the words ‘less than’, or ‘greater than’?

1. The individuals were randomly selected.

2. The sample average is normally distributed.

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

A. Probability info from theory.

1. Relevant info from problem

2. Sample info from problem

3. Population info as a result

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

A.  

Population info as a result.

B.  

Probability info from theory.

C.  

Relevant info from problem.

D.  

Sample info from problem.

A: Abstract.

1: Theorize.

2: Analyze.

3: Infer.

Statistic = t0.

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

The currently believed value of the population mean.

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

The researcher’s 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?

1. A middle body area

2. A left-tail area

3. A right-tail area

4. A two-tail area

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

A.  

A two-tail area.

B.  

A middle body area.

C.  

A left-tail area.

D.  

A right-tail area.

1. Acceptance Region.

2. Less than Rejection Region.

3. Greater than Rejection Region.

4. Not-Equal-To Rejection Region.

The critical value/From the z,t-Table

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?

From the t-equation (t0=¯x−μs√n).

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

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

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

The Type-II Error increases.

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

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

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

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

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