Deck 12: Experimental Design and Analysis of Variance

Question 1

When we carry out a chi-square test of independence,the chi-square statistic is based on (r × c)− 1 degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.

Answer 1

False

Question 2

When using a chi-square goodness-of-fit test with multinomial probabilities,the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.

Answer 2

True

Question 3

A multinomial probability distribution describes data that are classified into two or more categories when a multinomial experiment is carried out.

Answer 3

True

Question 4

In performing a chi-square test of independence,as the difference between the respective observed and expected frequencies calculated by assuming independence decreases,the probability of concluding that the row variable is independent of the column variable decreases.

Question 5

The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

Question 6

When we carry out a chi-square test of independence,the expected frequencies are based on the null hypothesis.

Question 7

The chi-square distribution is a continuous probability distribution that is skewed to the left.

Question 8

A contingency table summarizes data that has been classified on two dimensions or scales.

Question 9

In performing a chi-square goodness-of-fit test with multinomial probabilities,the smaller the difference between observed and expected frequencies,the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

Question 10

When using the chi-square goodness-of-fit test,if the value of the chi-square statistic is large enough,we reject the null hypothesis.

Question 11

When we carry out a chi-square test of independence,if r_i is the row total for row i and c_j is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.

Question 12

The chi-square goodness-of-fit test can only be used to test whether a population has specified multinomial probabilities or to test if a sample has been selected from a normally distributed population.It cannot be used if sample data come from other distribution forms,such as the Poisson.

Question 13

The χ² goodness-of-fit test requires the nominative level of data.

Question 14

A fastener manufacturing company uses a chi-square goodness-of-fit test to determine if a population of all lengths of ¼-inch bolts it manufactures is distributed according to a normal distribution.If we reject the null hypothesis,it is reasonable to assume that the population distribution is at least approximately normally distributed.

Question 15

In a contingency table,when all the expected frequencies equal the observed frequencies,the calculated χ² statistic equals zero.

Question 16

One use of the chi-square goodness-of-fit test is to determine if specified multinomial probabilities in the null hypothesis are correct.

Question 17

Expected cell frequencies for a multinomial distribution are calculated by assuming statistical dependence.

Question 18

When we carry out a chi-square test of independence,in the alternative hypothesis we state that the two classifications are statistically independent.

Question 19

In a contingency table,if all of the expected frequencies equal the observed frequencies,then we can conclude that there is a perfect association between rows and columns.

Question 20

The trials of a multinomial probability are assumed to be dependent.

Question 21

When we carry out a chi-square test of independence,as the differences between the respective observed and expected frequencies decrease,the probability of concluding that the row variable is independent of the column variable

A) decreases.
B) increases.
C) may decrease or increase depending on the number of rows and columns.
D) will be unaffected.

Question 22

In performing a chi-square goodness-of-fit test for a normal distribution,if there are 7 intervals,then the number of degrees of freedom for the chi-square statistic is ______.

A) 7
B) 3
C) 4
D) 6

Question 23

A special version of the chi-square goodness-of-fit test that involves testing the null hypothesis that all of the multinomial probabilities are equal is called the test for ___________.

A) goodness of fit
B) statistical independence
C) normality
D) homogeneity

Question 24

When we carry out a goodness-of-fit chi-square test,the expected frequencies are based on the alternative hypothesis.

Question 25

While a binomial distribution describes count data that can be classified into one of two mutually exclusive categories,a __________________ distribution describes count data that are classified into more than two mutually exclusive categories.

A) normal
B) skewed
C) uniform
D) multinomial

Question 26

In performing a chi-square goodness-of-fit test for a normal distribution,a researcher wants to make sure that all of the expected cell frequencies are at least five.The sample is divided into 7 intervals.The second through the sixth intervals all have expected cell frequencies of at least five.The first and the last intervals have expected cell frequencies of 1.5 each.After adjusting the number of intervals,the degrees of freedom for the chi-square statistic is ____.

A) 2
B) 3
C) 5
D) 7

Question 27

The chi-square goodness-of-fit test will be valid if the average of the expected cell frequencies is ______________.

A) greater than 0
B) less than 5
C) between 0 and 5
D) at least 1
E) at least 5

Question 28

Which,if any,of the following statements about the chi-square test of independence is false?

A) If r_i is the row total for row i and c_j is the column total for column j,then the estimated expected cell frequency corresponding to row i and column j equals (r_i)(c_j)/n.
B) The test is valid if all of the estimated cell frequencies are at least five.
C) The chi-square statistic is based on (r − 1)(c − 1)degrees of freedom,where r and c denote,respectively,the number of rows and columns in the contingency table.
D) The alternative hypothesis states that the two classifications are statistically independent.
E) All of the other statements about the chi-square test of independence are true.

Question 29

In performing a chi-square goodness-of-fit test with multinomial probabilities,the ___________ the difference between observed and expected frequencies,the higher the probability of concluding that the probabilities specified in the null hypothesis are correct.

A) larger
B) smaller

Question 30

As the difference between observed frequency and expected frequency _______________,the probability of rejecting the null hypothesis increases.

A) stays the same
B) decreases
C) increases
D) goes to 0

Question 31

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,we performed a chi-square test to determine whether the quality of the items produced appears to be the same for all three processes.What is the null hypothesis?

A) H₀: The number of defectives produced is independent of the production process used.
B) H₀: The row and column variables are associated with each other.
C) H₀: The proportion of defective units produced by the three production processes is the same.
D) Both "H₀: The number of defectives produced is independent of the production process used." and "H₀: The proportion of defective units produced by the three production processes is the same." are correct or at least acceptable ways of stating the null hypothesis.
E) All of the other choices are acceptable ways of stating the null hypothesis.

Question 32

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,we performed a chi-square test of independence to determine if the quality of the items produced appears to be independent of the production process.What are the degrees of freedom for the chi-square statistic?

A) 2
B) 3
C) 50
D) 520
E) 570

Question 33

When we carry out a chi-square goodness-of-fit test for a normal distribution,the null hypothesis states that the population

A) does not have a normal distribution.
B) has a normal distribution.
C) has a chi-square distribution.
D) does not have a chi-square distribution.
E) has k − 3 degrees of freedom.

Question 34

An experiment consists of 400 observations and four mutually exclusive groups.If the probability of a randomly selected item being classified into any of the four groups is equal,then the expected number of items that will be classified into group 1 is _____.

A) 25
B) 100
C) 125
D) 150

Question 35

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.What is the rejection point condition?

A) Reject H₀ if χ² > .10257
B) Reject H₀ if χ² > 9.3484
C) Reject H₀ if χ² > 5.99147
D) Reject H₀ if χ² > 7.37776
E) Reject H₀ if χ² > 7.81473

Question 36

The chi-square goodness-of-fit test for multinomial probabilities with 5 categories has _____ degrees of freedom.

A) 5
B) 4
C) 3
D) 6

Question 37

The χ² statistic from a contingency table with 6 rows and 5 columns will have

A) 30 degrees of freedom.
B) 24 degrees of freedom.
C) 5 degrees of freedom.
D) 20 degrees of freedom.
E) 25 degrees of freedom.

Question 38

In performing a chi-square test of independence,as the differences between respective observed and expected frequencies _________,the probability of concluding that the row variable is independent of the column variable increases.

A) stay the same
B) decrease
C) increase
D) double

Question 39

When we carry out a chi-square test of independence,the alternate hypothesis states that the two relevant classifications

A) are mutually exclusive.
B) form a contingency table with r rows and c columns.
C) have (r − 1)(c − 1)degrees of freedom.
D) are statistically dependent.
E) are normally distributed.

Question 40

The number of degrees of freedom associated with a chi-square test for independence based upon a contingency table with 4 rows and 3 columns is _____.

A) 7
B) 12
C) 5
D) 6

Question 41

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.Chi-Square Contingency Table Test for Independence At a significance level of .10,the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used.Based on the results summarized in the MegaStat/Excel output provided in the table above,we

A) do not reject H₀ and conclude that the quality of the product is not the same for all processes.
B) reject H₀ and conclude that the quality of the product is dependent on the manufacturing process.
C) do not reject H₀,and conclude that the quality of the product does not significantly differ among the three processes.
D) reject H₀ and conclude that the quality of the product is independent of the production process utilized.

Question 42

A study of car accidents and drivers who use cell phones collects the following sample data. Determine the expected frequencies of those who had accidents in the last year to use for the chi-square test of independence.

Question 43

A paper presented at a recent meeting of higher education researchers compared the type of college freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results. Calculate the chi-square statistic for this test of independence.

Question 44

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.Calculate the expected number of defective units produced by Process 1.

Question 45

A study of car accidents and drivers who use cell phones collects the following sample data. At a significance level of 0.05,determine the appropriate degrees of freedom and the rejection point condition for the test.

Question 46

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness-of-fit test for normal distribution.The results are summarized in the following table. At a significance level of .05,we

A) reject H₀;conclude that the residential home selling prices are not distributed according to a normal distribution.
B) do not reject H₀;conclude that the residential home selling prices are not distributed according to a normal distribution.
C) reject H₀;conclude that the residential home selling prices are distributed according to a normal distribution.
D) do not reject H₀;conclude that the residential home selling prices are distributed according to a normal distribution.

Question 47

A study of car accidents and drivers who use cell phones collects the following sample data. Determine the expected frequencies of those who had accidents in the last year to use for the chi-square test of independence.

Question 48

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness-of-fit test for normal distribution.The results are summarized in the following table. What is the appropriate null hypothesis?

A) H₀: The residential home selling prices are distributed according to a normal distribution.
B) H₀: The residential home selling prices are not distributed according to a normal distribution.
C) H₀: The distribution of residential home selling prices is either right or left skewed.
D) H₀: The distribution of the residential home selling prices is symmetric.
E) None of the other answers is correct.

Question 49

A study of car accidents and drivers who use cell phones collects the following sample data. Calculate the chi-square statistic for this test of independence.

Question 50

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness-of-fit test for normal distribution.The results are summarized in the following table. At a significance level of .05,what is the appropriate rejection point condition?

A) Reject H₀ if χ² > 12.5916
B) Reject H₀ if χ² > 11.0705
C) Reject H₀ if χ² > 9.3484
D) Reject H₀ if χ² > 7.81473
E) Reject H₀ if χ² > 9.48773

Question 51

Consider the 3 × 2 contingency table below. Compute the expected frequencies in row 1.

Question 52

A real estate company is analyzing the selling prices of residential homes in a given community.140 homes that have been sold in the past month are randomly selected and their selling prices are recorded.The statistician working on the project has stated that in order to perform various statistical tests,the data must be distributed according to a normal distribution.In order to determine whether the selling prices of homes included in the random sample are normally distributed,the statistician divides the data into 6 classes of equal size and records the number of observations in each class.She then performs a chi-square goodness-of-fit test for normal distribution.The results are summarized in the following table What are the degrees of freedom for the chi-square test?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 53

Consider the 3 × 2 contingency table below. Compute the expected frequencies in row 3.

Question 54

Consider the 3 × 2 contingency table below. Compute the expected frequencies in row 2.

Question 55

A paper presented at a recent meeting of higher education researchers compared the type of college that freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results. Determine the expected frequencies for the freshmen who drop out of 2-year institutions that will be used in the chi-square test of independence.

Question 56

A paper presented at a recent meeting of higher education researchers compared the type of college that freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results. At a significance level of .05,determine the appropriate degrees of freedom and the rejection point condition for this test.

Question 57

A paper presented at a recent meeting of higher education researchers compared the type of college that freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results. Determine the expected frequencies for the two cells of 4-year public institutions that will be used in the chi-square test of independence.

Question 58

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.Chi-Square Contingency Table Test for Independence At a significance level of .05,the management wants to perform a hypothesis test to determine if the quality of the items produced appears to be independent of the production process used.Based on the results summarized in the MegaStat/Excel output provided in the table above,we

A) reject H₀ and conclude that the quality of the product is not the same for all processes.
B) reject H₀ and conclude that the quality of the product is dependent on the manufacturing process.
C) do not reject H₀,and conclude that the quality of the product does not significantly differ among the three processes.
D) do not reject H₀,and conclude that the quality of the product is not the same for all processes.
E) reject H₀ and conclude that the quality of the product is independent of the manufacturing process used.

Question 59

A paper presented at a recent meeting of higher education researchers compared the type of college freshmen attend and the numbers who drop out.A random sample of freshmen shows the following results. Use a significance level of .05 and determine if the type of school and the drop rate are independent.(Null hypothesis is that dropout rate is independent of type of school. )

Question 60

Consider the 3 × 2 contingency table below. How many degrees of freedom are associated with the chi-square test?

Question 61

The AAA Co.is interested in the level of satisfaction of their employees in the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below.Very Satisfied

A survey was conducted of 125 AAA employees with the following results.

Using the critical value for α = .05,test the null hypothesis that the distribution of AAA employees at each satisfaction level is similar to the distribution of the employees of their major competitors.

Question 62

A survey was conducted on the age and gender of the purchasers of a specific automotive model.The results are below.
Test the null hypothesis that age is independent of gender at α = .05.

Question 63

AAA Co.operates distribution centers in the Midwest.Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures.According to the auditing firm,a billing had an equal probability of being from each of the three centers.A random sample of the audited billings had the following distribution.Center 1: 385 billings
Center 2: 305 billings
Center 3: 210 billings
What is the critical value at α = .01 to test the null hypothesis (equal billings from each center)?

Question 64

The AAA Co.is interested in the level of satisfaction of their employees with the benefit package that they offer compared to their major competitors.A consultant hired to conduct the satisfaction survey told AAA Co.that the distribution of level of satisfaction at other companies is displayed below.Very Satisfied

A survey of 125 AAA employees gave the following results.

What are the degrees of freedom for testing the goodness of fit at α = .05?

Question 65

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job.An exam was given to 120 employees.The results are below. For each cell,calculate the corresponding cell,row,and column percentage.

Question 66

The distance (in thousands of miles)traveled by buses before their first major motor failure is distributed below,with an estimated mean and standard deviation of 95.7 and 38.1.Also shown are the expected frequencies of these intervals if the original population was a normal distribution. What is the df for testing the hypothesis that the original population is a normal distribution?

Question 67

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job.An exam was given to 120 employees.The results are below. For each row total,calculate the corresponding percentage.

Question 68

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market. The estimated mean is 36.25,and the estimated standard deviation is 13.57.Calculate the expected frequencies for each interval,assuming a normal distribution.

Question 69

AAA Co.operates distribution centers in the Midwest.Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures.According to the auditing firm,a billing had an equal probability of being from each of the three centers.A random sample of the audited billings had the following distribution.Center 1: 385 billings
Center 2: 305 billings
Center 3: 210 billings
What are the degrees of freedom for the χ² test?

Question 70

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market. The estimated mean is 36.25,and the estimated standard deviation is 13.57.Calculate the value of the chi-square test statistic to determine whether these measurements came from a normal population. χ² = (10 − .24)²/.24 + (21 − 22.458)²/22.458 + (10 − 15.51)²/15.51 + (8 − 12.27)²/12.27
+ (5 − 6.732)²/6.732 + (6 − 2.79)²/2.79 = 404.58

Question 71

AAA Co.operates distribution centers in the Midwest.Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures.According to the auditing firm,a billing had an equal probability of being from each of the three centers.A random sample of the audited billings had the following distribution.Center 1: 385 billings
Center 2: 305 billings
Center 3: 210 billings
What is the expected value of the number of billings for each center if H₀ (equal probabilities)is true?

Question 72

A survey was conducted on the age and gender of the purchasers of a specific automotive model.The results are below.
For each column total,calculate the corresponding percentage.

Question 73

A survey was conducted on the age and gender of the purchasers of a specific automotive model.The results are below.
For each row total,calculate the corresponding percentage.

Question 74

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job.An exam was given to 120 employees.The results are below. For each column total,calculate the corresponding percentage.

Question 75

A survey was conducted on the age and gender of the purchasers of a specific automotive model.The results are below.
For each cell,calculate the corresponding cell,row,and column percentage.

Question 76

A manufacturing company produces part QV2Y for the aerospace industry.This particular part can be manufactured using 3 different production processes.The management wants to know if the quality of the units of part QV2Y is the same for all three processes.The production supervisor obtained the following data: Process 1 had 29 defective units in 240 items,Process 2 produced 12 defective units in 180 items,and Process 3 manufactured 9 defective units in 150 items.At a significance level of .05,the management wants to perform a hypothesis test to determine whether the quality of items produced appears to be independent of the production process used.Calculate the expected number of conforming units produced by Process 2.

Question 77

The HR manager of a major office supply chain is interested in determining whether employee educational level affects knowledge of their job.An exam was given to 120 employees.The results are below. Test the null hypothesis that score is independent of education level at α = .01.

Question 78

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market. The estimated mean is 36.25,and estimated standard deviation is 13.57.Calculate the probability for each interval,assuming a normal distribution.

Question 79

The following frequency table summarizes the ages of 60 shoppers at the local farmer's market The estimated mean is 36.25,and the estimated standard deviation is 13.57.It is desired to test whether these measurements came from a normal population.What is the df for this chi-square test of normality?

Question 80

AAA Co.operates distribution centers in the Midwest.Three of their centers were recently audited to determine if they are in compliance with company standard billing procedures.According to the auditing firm,a billing had an equal probability of being from each of the three centers.A random sample of the audited billings had the following distribution.Center 1: 385 billings
Center 2: 305 billings
Center 3: 210 billings
State the null hypothesis that states the expectations of the auditors.