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?

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?

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?

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?

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?

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?

all these other choices

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

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

A. hypothesis testing

B. confidence intervals

estimate the population mean?

test for the population mean?

estimate the population mean is confidence intervals, test for the population mean is hypothesis testing

What is the end result of the confidence interval method?

an interval estimate of the population mean

What is the end result of the hypothesis test method?

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

A. abstract problem information

B. theorize probability information

C. infer population information

D. analyze sample information

Step A?

Step 1?

Step 2?

Step 3?

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?

get descriptive statistics, write the two hypotheses

What is the primary task in Step 2: Analyze?

choose the appropriate equation

What is the primary task in Step 2: Analyze?

choose the appropriate equation

What is the end result of Step 3: Infer?

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?

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?

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?

summarize the question text into a reasonable size

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. n/a

B. 0.5

C. 25

D. 0.55

μ?

σ,s?

n?

x?

μ = 0.5, σ,s= n/a, n= 25, x= 0.55

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 1.15cm

A. 0.01

B. 1.15

C. 1.2

D. n/a

E. 37

μ?

σ?

n?

x?

s?

μ= 1.2, σ= 0.01, n= 37, x= 1.15, 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

A. 215,816

B. 58

C. 21,500

D. 23,500

E. 235,000

μ?

σ?

n?

x?

s?

μ= 215,816, σ=21,500, n=58, x=235,000, s=23,500

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. 1.7

B. 3,412

C. 0.7

D. n/a

μ,σ?

n?

x?

s?

μ,σ= n/a, n= 3,412, x=1.7, s=0.7

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

that all americans spend 4.5 hours

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

alpha (α)

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. 3.7

C. n/a

μ?

σ?

n,¯x,s?

μ= 23, σ=3.7, n,¯x,s=n/a

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. n/a

B. 14

C. 12

μ?

n,σ,s?

x?

μ= 14, n,σ,s=n/a, x=12

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. 5.3

B. 14

C. 1.2

D. 0.7

E. 4.1

μ?

σ?

n?

x?

s?

μ= 4.1, σ= 0.7, n=14, x=5.3, s=1.2

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. 83%

B. 25

C. 10%

D. n/a

E. 30

F. 78%

G. 13%

μ,σ?

n1?

n2?

x1?

x2?

s1?

s2?

μ,σ= n/a, n1= 30, n2=1 N² 25, x1=78%, x2=83%, s1= 10%, s2=13%

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

μ?

σ?

n,¯x,s?

μ=17, σ=10.5, n,¯x,s=n/a

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

the z-table, this z-equation: z=x−μ/σ/√n

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

A. Solve for the answer

B. Load the problem

C. Calibrate the x-Axis

D. Draw the schematic

Step 1?

Step 2?

Step 3?

Step 4?

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?

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?

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.

A. Confidence Interval

B. Sample Average

Point?

Interval?

point: sample average, 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?

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?

it uses the most information from the distribution of the data values

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

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?

sample average (¯x)

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

the margin of error

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

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).

A. Narrower (n)

B. Narrower (CL)

C. Wider (CL)

D. Wider (n)

Increase sample size?

Decrease sample size?

Increase level of confidence?

Decrease level of confidence?

increase sample size: narrower (n), decrease sample size: wider (n), increase level of confidence: wider (CL), 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?

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?

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?

the critical values

What is the size of the significance region?

alpha (α)

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

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.

A. Almost never

B. CL percent of the time

C. Always never

Sample average?

Confidence interval?

Sample standard deviation?

sample average= almost never, confidence interval= CL percent of the time, 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.

A. The value of the sample average

B. The value of the margin of error

Middle?

Spread?

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?

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?

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?

the logic for the sampling distribution of the sample average

Is the interval shown below properly detonated for a confidence interval?

(115,97)

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?

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.

A. a range of likely values for the sample average

B. a range of likely values for the population mean

the population mean?

the sample average?

the population mean= a range of likely values for the sample average, 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.

true

What is the main strength of a confidence interval?

gives a range of likely values for the population mean

What is the major weakness of a confidence interval?

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?

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?

α=1−CL

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

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?

critical value=2.080

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

critical value=1.697

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

critical value=3.250

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

CI%=¯x±t(α/2,n−1)(s√n)

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?

half the width of a confidence interval

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

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?

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?

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?

(96,118)

values= 107/11

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

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’.

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?

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?

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.

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.

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.

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. ?

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?

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?

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?

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?

(85,115)

yes, at the sample average is the best point estimator of the population mean

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?

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?

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?

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?

CI = (14.97, 17.02)

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

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

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

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’?

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

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

A. population info as a result

B. sample info from problem

C. probability info from theory

D. relevant info from problem

A: abstract?

1: theorize?

2: analyze?

3: infer?

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

statistic = t0

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

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?

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

A. a right-tail area

B. a left-tail area

C. a middle body area

D. a two-tail area

acceptance region?

less than rejection region?

greater than rejection region?

not-equal-to rejection region?

acceptance region— a middle body area, less than rejection region— a left-tail area, greater than rejection region— a right-tail area, 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?

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?

from the t-equation (t0=¯x−μs√n).

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

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?

the type-II error increases

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

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?

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