Deck 15: Design of Experiments and Analysis of Variance Anova

Question 1

Consider the following to answer the question(s) below:
A national car rental company recently conducted a study in which cars with automatic and standard transmissions were rented to male and female customers. Three customers in each category were randomly selected and the miles driven per day was recorded as follows:

Based on the design of this study, how many degrees of freedom will be associated with the mean squares for the type of transmission?

A) 1
B) 2
C) 3
D) 6
E) 8

Answer 1

A

Question 2

A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.
a. What are the null and alternative hypotheses (in words, not symbols)?
b. Are the conditions / assumptions for ANOVA met?
c. Calculate the F-statistic.
d. The P-value for this statistic turns out to be < .001. State the conclusion.
e. Suppose the company is concerned about whether different batches of green vegetable material would blanch differently. Suggest how the design for the study could have been improved to take this into account.

Answer 2

a. H0 : Mean vitamin A retention amounts are equal across the three blanching processes.
HA : Mean vitamin A retention amounts are not all equal across the three blanching processes.
b. We need to assume that the vegetable material samples were randomly assigned to the processes. Boxplots of the original data indicate that the equal variance assumption is reasonable. The normal probability plot of residuals indicates that the normality assumption is reasonable.
c. F = 23.27
d. With such a small P-value, we can reject the null hypothesis and conclude that mean vitamin A retention amounts are not all equal across the different blanching processes.
e. A randomized block design using batch as the blocking variable could improve the study.

Question 3

Consider the following to answer the question(s) below:
Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

Suppose that employees fall into several job categories, such as clerical, technical, or professional. Which of the following statements is true?

A) Job category is not a confounding variable.
B) Job category may be an outlier variable.
C) A randomized block design using job category as the blocking variable cannot improve the study.
D) Job category may be a confounding variable, and a randomized block design using job category as the blocking variable might improve the study.
E) Job category may be an outlier variable, and a randomized block design using job category as the blocking variable cannot improve the study.

Answer 3

D

Question 4

Consider the following to answer the question(s) below:
Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

The correct null hypothesis is

A) Mean employee job satisfaction ratings are equal across companies with different management styles.
B) Mean employee job satisfaction ratings are not all equal across companies with different management styles.
C) Management styles do not affect employee job satisfaction ratings.
D) Mean employee job satisfaction ratings are equal across companies with different management styles and that management styles do not affect employee job satisfaction ratings.
E) Mean employee job satisfaction ratings are not all equal across companies with different management styles and that management styles do not affect employee job satisfaction ratings.

Question 5

Consider the following to answer the question(s) below:
A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.

The F-statistic value is

A) F = 23.367
B) F = 2.215
C) F = 27.57
D) F = 7.999
E) F = 3.22

Question 6

Consider the following to answer the question(s):
An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. They take a random sample of executives in three different industries: (1 = Consumer Goods, 2 = Financial, 3 = Health Care). Salary data are collected. The two-way ANOVA results appear below.
At α = 0.05, we can conclude

A) that mean executive salaries are the same across the three different industry sectors
B) that mean executive salaries are the same for males and females
C) that there is a significant interaction effect
D) that mean executive salaries are not the same across the three different industry sectors and that mean executive salaries are not the same for males and females
E) that mean executive salaries are the same across the three different industry sectors, are the same for males and females and that there is a significant interaction effect

Question 7

Consider the following to answer the question(s) below:
An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following is partial Excel output for the data.

The P-value for this statistic is < 0.001. Therefore, at α = 0.05

A) We reject the null hypothesis and conclude that the average weekly connect times are not the same for all three methods of connection.
B) We fail to reject the null hypothesis.
C) We know average connect times are the same for all connection methods.
D) We fail to reject the null hypothesis and conclude that the average weekly connect times are the same for all three methods of connection.
E) We know average connect times are not the same for all connection methods.

Question 8

Consider the following to answer the question(s) below:
Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

The F-statistic value is

A) F = 35.16
B) F = 2.604
C) F = 48.7
D) F = 1.385
E) F = 3.60

Question 9

Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.
a. What are the null and alternative hypotheses (in words, not symbols)?
b. Are the conditions / assumptions for ANOVA met?
c. Calculate the F-statistic.
d. The P-value for this statistic turns out to be < .001. State the conclusion.
e. Suppose that employees fall into several job categories, such as clerical, technical, or professional. How might this affect the study results? Suggest how the design for the study could have been improved.

Question 10

Consider the following to answer the question(s) below:
Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

A survey of online consumers asked respondents to indicate how much money they spent for online purchases during the most recent Christmas holiday season. These data were analyzed to see if gender and income level influence the amount consumers spend online for holiday shopping. The two way ANOVA results appear below. Which of the following statements is true?

A) This is an experiment.
B) This is a randomized block design.
C) Since the interaction effect of gender and income level on online expenditure is significant, it is not appropriate to interpret the main effects due to gender and income level separately.
D) This is an experiment and since the interaction effect of gender and income level on online expenditure is significant, it is not appropriate to interpret the main effects due to gender and income level separately.
E) This is a randomized block design and since the interaction effect of gender and income level on online expenditure is significant, it is not appropriate to interpret the main effects due to gender and income level separately.

Question 11

Consider the following to answer the question(s) below:
An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following is partial Excel output for the data.

In a completely randomized design, which of the following is true?

A) The mean squares due to treatments will be larger than the mean squares due to error if the null hypothesis is rejected.
B) The mean squares due to treatments will be smaller than the mean squares due to error if the null hypothesis is rejected.
C) The sum of squares due to treatments will be equal to the sum of squares due to error if the null hypothesis is rejected.
D) The populations must have equal means.
E) The sample sizes must be equal.

Question 12

An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. They take a random sample of executives in three different industries: (1 = Consumer Goods, 2 = Financial, 3 = Health Care). Salary data are collected. The two-way ANOVA results appear below. a. Is this an experiment or observational study?
b. Are the conditions for two-way ANOVA met?
c. If so, perform the hypothesis tests and state your conclusions in terms of amount spent online, gender, and income level.
d. Is it appropriate to interpret the main effects in this case? Explain.

Question 13

Consider the following to answer the question(s) below:
A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.

The P-value for this statistic turns out to be < 0.001. Therefore, at α = 0.05

A) We fail to reject the null hypothesis.
B) We reject the null hypothesis.
C) We conclude that mean vitamin A retention amounts are not all equal across the different blanching processes.
D) We fail to reject the null hypothesis and conclude that mean vitamin A retention amounts are not all equal across the different blanching processes..
E) We reject the null hypothesis and conclude that mean vitamin A retention amounts are not all equal across the different blanching processes.

Question 14

Consider the following to answer the question(s) below:
A national car rental company recently conducted a study in which cars with automatic and standard transmissions were rented to male and female customers. Three customers in each category were randomly selected and the miles driven per day was recorded as follows:

Given the following output, which of the following statements is true at α = 0.05?

A) Since the interaction effect of gender and transmission type on miles driven is not significant, it is appropriate to interpret the main effects due to gender and transmission type separately.
B) We reject the hypothesis that gender affects miles driven per day.
C) Since the interaction effect of gender and transmission type on miles driven is significant, it is not appropriate to interpret the main effects due to gender and transmission type separately.
D) We reject the hypothesis that transmission type influences miles driven per day.
E) Both gender and transmission influence the number of miles drive per day.

Question 15

Consider the following to answer the question(s) below:
A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They are examining three different blanching processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below.

The correct null hypothesis is

A) Mean vitamin A retention amounts are not all equal across the three blanching processes.
B) Mean vitamin A retention amounts are equal across the three blanching processes.
C) Blanching process has an effect on vitamin A retention.
D) Mean vitamin A retention amounts are not all equal across the three blanching processes, and the blanching process has an effect on vitamin A retention.
E) Mean vitamin A retention amounts are equal across the three blanching processes, and the blanching process has an effect on vitamin A retention.

Question 16

Consider the following to answer the question(s):
An advocacy group is interested in determining if gender (1 = Female, 2 = Male) affects executive level salaries. They take a random sample of executives in three different industries: (1 = Consumer Goods, 2 = Financial, 3 = Health Care). Salary data are collected. The two-way ANOVA results appear below.
Which of the following statements is true?

A) This is an experiment.
B) This is an observational study.
C) This is a randomized block design.
D) This is an experimental study involving a randomized block design.
E) This is an observational study involving a randomized block design.

Question 17

Consider the following to answer the question(s) below:
An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following is partial Excel output for the data.

The correct null hypothesis is

A) Mean weekly connect times are equal regardless of the method of connection.
B) Mean weekly connect times are not equal regardless of the method of connection.
C) Method of internet connection has no impact on average weekly connect times.
D) Method of internet connection has an impact on average weekly connect times.
E) None of the above.

Question 18

Consider the following to answer the question(s) below:
An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following is partial Excel output for the data.

The F-statistic value is

A) 43.88
B) 962.72
C) 21.94
D) 0.02
E) 3.554

Question 19

A survey of online consumers asked respondents to indicate how much money they spent for online purchases during the most recent Christmas holiday season. These data were analyzed to see if gender and income level (1 = Low, 2 = Middle, 3 = High) influence the amount consumers spend online for holiday shopping. The two way ANOVA results appear below. a. Is this an experiment or observational study?
b. Are the conditions for two-way ANOVA met?
c. If so, perform the hypothesis tests and state your conclusions in terms of amount spent online, gender and income level.
d. Is it appropriate to interpret the main effects in this case? Explain.

Question 20

Consider the following to answer the question(s) below:
Management styles differ among organizations and may potentially affect employee job satisfaction. A sample of employees was randomly selected from each of three companies with different management styles (Authoritarian, Laissez faire and Participative) and asked to rate their level of job satisfaction on a 10-point scale (10 being the highest level of satisfaction). The data collected and partial ANOVA results appear below.

The P-value for this statistic turns out to be < 0.001. Therefore, at α = 0.05

A) We fail to reject the null hypothesis.
B) We reject the null hypothesis and conclude that mean employee job satisfaction ratings are not all equal across companies with different management styles.
C) We conclude that mean employee job satisfaction ratings are all equal across companies with different management styles.
D) We fail to reject the null hypothesis and conclude that mean employee job satisfaction ratings are all equal across companies with different management styles.
E) We reject the null hypothesis and conclude that mean employee job satisfaction ratings are all equal across companies with different management styles.

Question 21

Consider the following to answer the question(s) below:
To test the fuel efficiency of three new car models, random samples of twenty were selected from each of the models and litres/100 kilometres data obtained. Partial output follows.

What is the mean square due to treatments?

A) 0.82
B) 0.57
C) 0.03
D) 1.63
E) 0.55

Question 22

Consider the following to answer the question(s) below:
To test the fuel efficiency of three new car models, random samples of twenty were selected from each of the models and litres/100 kilometres data obtained. Partial output follows.

The correct value of the F test statistic is

A) 1.43
B) 0.70
C) 1.49
D) 0.50
E) 1.04

Question 23

Consider the following to answer the question(s) below:
To test the fuel efficiency of three new car models, random samples of twenty were selected from each of the models and litres/100 kilometres data obtained. Partial output follows.

What is the mean square due to the error?

A) 0.57
B) 0.82
C) 0.03
D) 0.55
E) 1.63

Question 24

Consider the following to answer the question(s) below:
A national car rental company recently conducted a study in which cars with automatic and standard transmissions were rented to male and female customers. Three customers in each category were randomly selected and the miles driven per day was recorded as follows:

Which of the following is not a principle of experimental design?

A) Balance
B) Control
C) Randomization
D) Blocking
E) Replication