Essentials of Statistics for Business & Economics

David R. Anderson; Dennis J. Sweeney; Thomas A. Williams; Jeffrey D. Camm; James J. Cochran

Chapter 13

Experimental Design and Analysis of Variance - all with Video Answers

Educators

Chapter Questions

Problem 1

$$
\begin{aligned}
&\text {The following data are from a completely randomized design. }\\
&
\end{aligned}
$$
a. Compute the sum of squares between treatments.
b. Compute the mean square between treatments.
c. Compute the sum of squares due to error.
d. Compute the mean square due to error.
e. Set up the ANOVA table for this problem.
f. At the $\alpha=.05$ level of significance, test whether the means for the three treatments are equal.

Kratika Bhadauria

Kratika Bhadauria

Numerade Educator

Problem 2

In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table.$$
\begin{array}{lccccc}
\begin{array}{l}
\text { Source } \\
\text { of Variation }
\end{array} & \begin{array}{l}
\text { Sum } \\
\text { of Squares }
\end{array} & \begin{array}{l}
\text { Degrees } \\
\text { of Freedom }
\end{array} & \begin{array}{l}
\text { Mean } \\
\text { Square }
\end{array} & \boldsymbol{F} & \boldsymbol{p} \text {-value }
\end{array}
$$

Sheryl Ezze

Numerade Educator

Problem 3

Refer to exercise 2.
a. What hypotheses are implied in this problem?
b. At the $\alpha=.05$ level of significance, can we reject the null hypothesis in part (a)? Explain.

Srikar Katta

Numerade Educator

Problem 4

In an experiment designed to test the output levels of three different treatments, the following results were obtained. $\mathrm{SST}=400, \mathrm{SSTR}=150, n_7=19$. Set up the ANOVA table and test for any significant difference between the mean output levels of the three treatments. $\mathrm{Use} \alpha=.05$.

Sheryl Ezze

Numerade Educator

Problem 5

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?$$
\begin{array}{lclllll}
\begin{array}{l}
\text { Source } \\
\text { of Variation }
\end{array} & \begin{array}{l}
\text { Sum } \\
\text { of Squares }
\end{array} & \begin{array}{l}
\text { Degrees } \\
\text { of Freedom }
\end{array} & \begin{array}{l}
\text { Mean } \\
\text { Square }
\end{array} & \text { F } & \text { p-value } \\
\begin{array}{ll}
\text { Treatments }
\end{array} & 1200 & & & & \\
\begin{array}{ll}
\text { Error }
\end{array} & 1800 & & & & \\
\text { Total } & & & & &
\end{array}
$$

Srikar Katta

Numerade Educator

Problem 6

Develop the analysis of variance computations for the following completely randomized design. At $\alpha=.05$, is there a significant difference between the treatment means?(TABLE CAN'T COPY)

Sheryl Ezze

Numerade Educator

Problem 7

Product Assembly. Three different methods for assembling a product were proposed by an industrial engineer. To investigate the number of units assembled correctly with each method, 30 employees were randomly selected and randomly assigned to the three proposed methods in such a way that each method was used by 10 workers. The number of units assembled correctly was recorded, and the analysis of variance procedure was applied to the resulting data set. The following results were obtained: $\mathrm{SST}=10,800 ;$ SSTR $=4560$.
a. Set up the ANOVA table for this problem.
b. Use $\alpha=.05$ to test for any significant difference in the means for the three assembly methods.

Srikar Katta

Numerade Educator

Problem 8

Testing Quality Awareness, Refer to the NCP data in Table 13.4. Set up the ANOVA table and test for any significant difference in the mean examination score for the three plants. Use $\alpha=.05$.

Sheryl Ezze

Numerade Educator

Problem 9

Temperature's Effect on a Chemical Process. To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Construct an analysis of variance table. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process.
(TABLE CAN'T COPY)

Srikar Katta

Numerade Educator

Problem 10

Auditing Errors. Auditors must make judgments about various aspects of an audit on the basis of their own direct experience, indirect experience, or a combination of the two. In a study, auditors were asked to make judgments about the frequency of errors to be found in an audit. The judgments by the auditors were then compared to the actual results. Suppose the following data were obtained from a similar study; lower scores indicate better judgments.$$
\begin{array}{ccc}
\text { Direct } & \text { Indirect } & \text { Combination } \\
17.0 & 16.6 & 25.2 \\
18.5 & 22.2 & 24.0 \\
15.8 & 20.5 & 21.5 \\
18.2 & 18.3 & 26.8 \\
20.2 & 24.2 & 27.5 \\
16.0 & 19.8 & 25.8 \\
13.3 & 21.2 & 24.2
\end{array}
$$
Use $\alpha=.05$ to test to see whether the basis for the judgment affects the quality of the judgment. What is your conclusion?

Sheryl Ezze

Numerade Educator

Problem 11

Paint-Drying Robots. How long it takes paint to dry can have an impact on the production capacity of a business. In May 2018, Deal's Auto Body \& Paint in Prescott, Arizona, irvested in a paint-drying robot to speed up its process (The Daily Courier website, https://www.dcourier.com/photos/2018/may/26/984960336/). An interesting question is, "Do all paint-drying robots have the same drying time?" To test this, suppose we sample five drying times for each of different brands of paint-drying robots. The time in minutes until the paint was dry enough for a second coat to be applied was recorded. The following data were obtained.$$
\begin{array}{cccc}
\text { Robot 1 } & \text { Robot 2 } & \text { Robot 3 } & \text { Robot 4 } \\
128 & 144 & 133 & 150 \\
137 & 133 & 143 & 142 \\
135 & 142 & 137 & 135 \\
124 & 146 & 136 & 140 \\
141 & 130 & 131 & 153
\end{array}
$$
At the $\alpha=.05$ level of significance, test to see whether the mean drying time is the same for each brand of robot.

Sheryl Ezze

Numerade Educator

Problem 12

Restaurant Satisfaction. The Consumer Reports Restaurant Customer Satisfaction Survey is based upon 148,599 visits to full-service restaurant chains (Consumer Reports website, https://www.consumerreports.org/cro/restaurants/buying-guide/index htm). One of the variables in the study is meal price, the average amount paid per person for dinner and drinks, minus the tip. Suppose a reporter for the Sun Coast Times thought that it would be of interest to her readers to conduct a similar study for restaurants located on the Grand Strand section in Myrtle Beach, South Carolina. The reporter selected a sample of 8 seafood restaurants, 8 Italian restaurants, and 8 steakhouses. The following data show the meal prices ( $$\$ $$ ) obtained for the 24 restaurants sampled. Use $\alpha=.05$ to test whether there is a significant difference among the mean meal price for the three types of restaurants.$$
\begin{array}{ccc}
\text { Italian } & \text { Seafood } & \text { Steakhouse } \\
\$ 12 & \$ 16 & \$ 24 \\
13 & 18 & 19 \\
15 & 17 & 23 \\
17 & 26 & 25 \\
18 & 23 & 21 \\
20 & 15 & 22 \\
17 & 19 & 27 \\
24 & 18 & 31
\end{array}
$$
a. At the $\alpha=.05$ level of significance, can we reject the null hypothesis that the means of the three treatments are equal?
b. Use Fisher's LSD procedure to test whether there is a significant difference between the means for treatments $A$ and $B$, treatments $A$ and $C$, and treatments $B$ and C. Use $\alpha=.05$.
c. Use Fisher's LSD procedure to develop a $95 \%$ confidence interval estimate of the difference between the means of treatments A and B .

Sheryl Ezze

Numerade Educator

Problem 13

$$
\begin{aligned}
&\text { The following data are from a completely randomized design. }\\
&\begin{array}{lccc}
& \text { Treatment } & \text { Treatment } & \text { Treatment } \\
& \text { A } & \text { B } & \text { C } \\
& 32 & 44 & 33 \\
& 30 & 43 & 36 \\
& 30 & 44 & 35 \\
& 26 & 46 & 36 \\
\text { Sample mean } & 32 & 48 & 40 \\
\text { Sample variance } & 30 & 45 & 36 \\
& 6.00 & 4.00 & 6.50
\end{array}
\end{aligned}
$$

Sheryl Ezze

Numerade Educator

Problem 14

The following data are from a completely randomized design. In the following calculations, use $\alpha=.05$.
a. Use analysis of variance to test for a significant difference among the means of the three treatments.
b. Use Fisher's LSD procedure to determine which means are different.

Sheryl Ezze

Numerade Educator

Problem 15

Testing Chemical Processes. To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material.$$
\begin{aligned}
&\text { Manufacturer }\\
&\begin{array}{ccc}
\mathbf{1} & \mathbf{2} & \mathbf{3} \\
20 & 28 & 20 \\
26 & 26 & 19 \\
24 & 31 & 23 \\
22 & 27 & 22
\end{array}
\end{aligned}
$$
a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use $\alpha=.05$.
b. At the $\alpha=.05$ level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. What conclusion can you draw after carrying out this test?

Sheryl Ezze

Numerade Educator

Problem 16

Confidence Intervals for Different Processes. Refer to exercise 15. Use Fisher's LSD procedure to develop a $95 \%$ confidence interval estimate of the difference between the means for manufacturer 1 and manufacturer 2 .

Sheryl Ezze

Numerade Educator

Problem 17

Marketing Ethics. In the digital age of marketing, special care must be taken to make sure that programmatic ads appearing on websites align with a company's strategy, culture and ethics. For example, in 2017, Nordstrom, Amazon and Whole Foods each faced boycotts form social media users when automated ads for these companies showed up on the Breitbart website (ChiefMarketercom). It is important for marketing professionals to understand a company's values and culture. The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals specializing in marketing (higher scores indicate higher ethical values).$$
\begin{array}{ccc}
\text { Marketing Managers } & \text { Marketing Research } & \text { Advertising } \\
6 & 5 & 6 \\
5 & 5 & 7 \\
4 & 4 & 6 \\
5 & 4 & 5 \\
6 & 5 & 6 \\
4 & 4 & 6
\end{array}
$$
a. Use $\alpha=.05$ to test for significant differences in perception among the three groups.
b. At the $\alpha=.05$ level of significance, we can conclude that there are differences in the perceptions for marketing managers, marketing research specialists, and advertising specialists. Use the procedures in this section to determine where the differences occur. Use $\alpha=.05$.

Dominador Tan

Numerade Educator

Problem 18

Machine Breakdowns. To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained.$$
\begin{array}{cccc}
\text { Machine 1 } & \text { Machine 2 } & \text { Machine 3 } & \text { Machine 4 } \\
6.4 & 8.7 & 11.1 & 9.9 \\
7.8 & 7.4 & 10.3 & 12.8 \\
5.3 & 9.4 & 9.7 & 12.1 \\
7.4 & 10.1 & 10.3 & 10.8 \\
8.4 & 9.2 & 9.2 & 11.3 \\
7.3 & 9.8 & 8.8 & 11.5
\end{array}
$$
a. At the $\alpha=.05$ level of significance, what is the difference, if any, in the population mean times among the four machines?
b. Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a . 05 level of significance.

Sheryl Ezze

Numerade Educator

Problem 19

Testing Time to Breakdown Between All Pairs of Machines. Refer to exercise 18. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experimentwise error rate of .05 is desired.

Beth Stone

Numerade Educator

Problem 20

Minor League Baseball Attendance. The International League of Triple-A minor league baseball consists of 14 teams organized into three divisions: North, South, and West. The following data show the average attendance for the 14 teams in the International League. Also shown are the teams' records; W denotes the number of games won, L denotes the number of games lost, and PCT is the proportion of games played that were won.$$
\begin{array}{lllllc}
\text { Team Name } & \text { Division } & \text { W } & \text { L } & \text { PCT } & \text { Attendance } \\
\text { Buffalo Bisons } & \text { North } & 66 & 77 & .462 & 8812 \\
\text { Lehigh Valley IronPigs } & \text { North } & 55 & 89 & .382 & 8479 \\
\text { Pawtucket Red Sox } & \text { North } & 85 & 58 & .594 & 9097 \\
\text { Rochester Red Wings } & \text { North } & 74 & 70 & .514 & 6913 \\
\text { Scranton-Wilkes Barre Yankees } & \text { North } & 88 & 56 & .611 & 7147 \\
\text { Syracuse Chiefs } & \text { North } & 69 & 73 & .486 & 5765 \\
\text { Charlotte Knights } & \text { South } & 63 & 78 & .447 & 4526 \\
\text { Durham Bulls } & \text { South } & 74 & 70 & .514 & 6995 \\
\text { Norfolk Tides } & \text { South } & 64 & 78 & .451 & 6286 \\
\text { Richmond Braves } & \text { South } & 63 & 78 & .447 & 4455 \\
\text { Columbus Clippers } & \text { West } & 69 & 73 & .486 & 7795 \\
\text { Indianapolis Indians } & \text { West } & 68 & 76 & .472 & 8538 \\
\text { Louisville Bats } & \text { West } & 88 & 56 & .611 & 9152 \\
\text { Toledo Mud Hens } & \text { West } & 75 & 69 & .521 & 8234
\end{array}
$$
a. Use $\alpha=.05$ to test for any difference in the mean attendance for the three divisions.
b. Use Fisher's LSD procedure to determine where the differences occur. Use $\alpha=.05$.

Sheryl Ezze

Numerade Educator

Problem 21

Consider the experimental results for the following randomized block design. Make the calculations necessary to set up the analysis of variance table.
(TABLE CAN'T COPY)
Use $\alpha=.05$ to test for any significant differences.

Shu Naito

Numerade Educator

Problem 22

The following data were obtained for a randomized block design involving five treatments and three blocks: SST $=430$, SSTR $=310$, SSBL $=85$. Set up the ANOVA table and test for any significant differences. Use $\alpha=.05$.

Sheryl Ezze

Numerade Educator

Problem 23

An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table.$$
\begin{array}{lcll}
\begin{array}{lc}
\text { Source } \\
\text { of Variation }
\end{array} & \begin{array}{l}
\text { Sum } \\
\text { of Squares }
\end{array} & \begin{array}{l}
\text { Degrees } \\
\text { of Freedom }
\end{array} & \begin{array}{l}
\text { Mean } \\
\text { Square }
\end{array} \\
\begin{array}{l}
\text { Treatments }
\end{array} & 900 & & \\
\begin{array}{l}
\text { Blocks }
\end{array} & 400 & & \\
\text { Error } & 1800 & & \\
\text { Total } & &
\end{array}
$$
Use $\alpha=.05$ to test for any significant differences.

Sheryl Ezze

Numerade Educator

Problem 24

Auto Tune-Ups. An automobile dealer conducted a test to determine if the time in minutes needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data obtained follow.
(TABLE CAN'T COPY)
Use $\alpha=.05$ to test for any significant differences.

Shu Naito

Numerade Educator

Problem 25

Airfares on Travel Websites. Are there differences in airfare depending on which travel agency website you utilize? The following data were collected on travel agency websites on July 9, 2018. The following table contains the prices in U.S. dollars for a one-way ticket between the cities listed on the left for each of the three travel agency websites. Here the pairs of cities are the blocks and the treatments are the different websites. Use $\alpha=.05$ to test for any significant differences in the mean price of a one-way airline ticket for the three travel agency websites.
(TABLE CAN'T COPY)

Shu Naito

Numerade Educator

Problem 26

SAT Performance. The Scholastic Aptitude Test (SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800 -point scale. A sample of SAT scores for six students follows.
$$
\begin{array}{cccc}
\text { Student } & \begin{array}{c}
\text { Critical } \\
\text { Reading }
\end{array} & \text { Mathematics } & \text { Writing } \\
1 & 526 & 534 & 530 \\
2 & 594 & 590 & 586 \\
3 & 465 & 464 & 445 \\
4 & 561 & 566 & 553 \\
5 & 436 & 478 & 430 \\
6 & 430 & 458 & 420
\end{array}
$$
a. Using a . 05 level of significance, do students perform differently on the three areas of the SAT?
b. Which area of the test seems to give the students the most trouble? Explain.

Shu Naito

Numerade Educator

Problem 27

Consumer Preferences. In 2018, consumer goods giant Procter and Gamble (P\&G) had more than 20 brands with more than $$\$ 1$$ billion in annual sales (P\&G website, https//hs.pg.com/). How does a company like P\&G create so many successful consumer products? P\&G effectively invests in research and development to understand what consumers want. One method used to determine consumer preferences is called conjoint analysis. Conjoint analysis allows a company to ascertain the utility that a respondent in the conjoint study places on a design of a given product. The higher the utility, the more valuable a respondent finds the design. Suppose we have conducted a conjoint study and have the following estimated utilities (higher is preferred) for each of three different designs for a new whitening toothpaste.$$
\begin{aligned}
&\\
&\text { At the } 05 \text { level of significance, test for any significant differences. }
\end{aligned}
$$
(TABLE CAN'T COPY)

Shu Naito

Numerade Educator

Problem 28

A factorial experiment involving two levels of factor $A$ and three levels of factor $B$ resulted in the following data.
(TABLE CAN'T COPY)
Test for any significant main effects and any interaction. Use $\alpha=.05$.

Dominador Tan

Numerade Educator

Problem 29

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B , and three replications resulted in the following data: $\mathrm{SST}=280$, $\mathrm{SSA}=26, \mathrm{SSB}=23, \mathrm{SSAB}=175$. Set up the ANOVA table and test for any significant main effects and any interaction effect. Use $\alpha=.05$.

Shu Naito

Numerade Educator

Problem 30

Mobile App Website Design. Based on a 2018 study, the average elapsed time between when a user navigates to a website on a mobile device until its main content is available was 14.6 seconds. This is more than a $20 \%$ increase from 2017 (searchenginejournal.com, https://www.searchenginejournal.com/). Responsiveness is certainly an important feature of any website and is perhaps even more important on a mobile device. What other web design factors need to be considered for a mobile device to make it more user friendly? Among other things, navigation menu placement and amount of text entry required are important on a mobile device. The following data provide the time it took (in seconds) randomly selected students (two for each factor combination) to perform a prespecified task with the different com-
(TABLE CAN'T COPY)
Use the ANOVA procedure for factorial designs to test for any significant effects resulting from navigation menu position and amount of text entry required. Use $\alpha=.05$.

Shu Naito

Numerade Educator

Problem 31

Amusement Park Queues. An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use $\alpha=.05$.
$$
\begin{array}{lccc}
& & \begin{array}{c}
\text { Type of Ride } \\
\text { Screaming Demon }
\end{array} & \text { Log Flume } \\
\text { Method 1 } & 41 & 52 & 50 \\
& 43 & 44 & 46 \\
\text { Method 2 } & 49 & 50 & 48 \\
& 51 & 46 & 44
\end{array}
$$

Shu Naito

Numerade Educator

Problem 32

Auto Fuel Efficiency. As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUVs). The following data show the miles-per-gallon rating Conswmer Reports obtained for two hybrid small cars, two hybrid midsize cars, two hybrid small SUVs, and two hybrid midsize SUVs; also shown are the miles per gallon obtained for eight similarly equipped conventional models.
$$
\begin{array}{lllc}
\text { Make/Model } & \text { Class } & \text { Type } & \text { MPG } \\
\text { Honda Civic } & \text { Small Car } & \text { Hybrid } & 37 \\
\text { Honda Civic } & \text { Small Car } & \text { Conventional } & 28 \\
\text { Toyota Prius } & \text { Small Car } & \text { Hybrid } & 44 \\
\text { Toyota Coralla } & \text { Small Car } & \text { Conventional } & 32 \\
\text { Chevrolet Malibu } & \text { Midsize Car } & \text { Hybrid } & 27 \\
\text { Chevrolet Malibu } & \text { Midsize Car } & \text { Conventional } & 23 \\
\text { Nissan Altima } & \text { Midsize Car } & \text { Hybrid } & 32 \\
\text { Nissan Altima } & \text { Midsize Car } & \text { Conventional } & 25 \\
\text { Ford Escape } & \text { Small SUV } & \text { Hybrid } & 27 \\
\text { Ford Escape } & \text { Small SUV } & \text { Conventional } & 21 \\
\text { Saturn Vue } & \text { Small SUV } & \text { Hybrid } & 28 \\
\text { Saturn Vue } & \text { Small SUV } & \text { Conventional } & 22 \\
\text { Lexus RX } & \text { Midsize SUV } & \text { Hybrid } & 23 \\
\text { Lexus RX } & \text { Midsize SUV } & \text { Conventional } & 19 \\
\text { Toyota Highlander } & \text { Midsize SUV } & \text { Hybrid } & 24 \\
\text { Toyota Highlander } & \text { Midsize SUV } & \text { Conventional } & 18 \\
& & &
\end{array}
$$
At the $\alpha=.05$ level of significance, test for significant effects due to class, type, and interaction.

Shu Naito

Numerade Educator

Problem 33

Tax Research. A study reported in The Accounting Review examined the separate and joint effects of two levels of time pressure (low and moderate) and three levels of knowledge (naive, declarative, and procedural) on key word selection behavior in tax research. Subjects were given a tax case containing a set of facts, a tax issue, and a key word index consisting of 1336 key words. They were asked to select the key words they believed would refer them to a tax authority relevant to resolving the tax case. Prior to the experiment, a group of tax experts determined that the text contained 19 relevant key words. Subjects in the naive group had little or no declarative or procedural knowledge, subjects in the declarative group had significant declarative knowledge but little or no procedural knowledge, and subjects in the procedural group had significant declarative knowledge and procedural knowledge. Declarative knowledge consists of knowledge of both the applicable tax rules and the technical terms used to describe such rules. Procedural knowledge is knowledge of the rules that guide the tax researcher's search for relevant key words. Subjects in the low time pressure situation were told they had 25 minutes to complete the problem, an amount of time which should be "more than adequate" to complete the case; subjects in the moderate time pressure situation were told they would have "only" 11 minutes to complete the case. Suppose 25 subjects were selected for each of the six treatment combinations and the sample means for each treatment combination are as follows (standard deviations are in parentheses).
(TABLE CAN'T COPY)
Use the ANOVA procedure to test for any significant differences due to time pressure, knowledge, and interaction. Use a . 05 level of significance. Assume that the total sum of squares for this experiment is 327.50 .

Shu Naito

Numerade Educator

Problem 34

Paper Towel Absorption. In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equal-size towels were used, with four sections of towels tested per brand. The absorbency rating data follow. At a .05 level of significance, does there appear to be a difference in the ability of the brands to absorb water?
(TABLE CAN'T COPY)

Rashmi Sinha

Numerade Educator

Problem 35

Job Satisfaction. A study reported in the Journal of Small Business Management concluded that self-employed individuals do not experience higher job satisfaction than individuals who are not self-employed. In this study, job satisfaction is measured using 18 items, each of which is rated using a Likert-type scale with 1-5 response options ranging from strong agreement to strong disagreement. A higher score on this scale indicates a higher degree of job satisfaction. The sum of the ratings for the 18 items, ranging from 18 to 90 , is used as the measure of job satisfaction. Suppose that this approach was used to measure the job satisfaction for lawyers, physical therapists, cabinetmakers, and systems analysts. The results obtained for a sample of 10 individuals from each profession follow.$$
\begin{array}{cccc}
\text { Lawyer } & \text { Physical Therapist } & \text { Cabinetmaker } & \text { Systems Analyst } \\
44 & 55 & 54 & 44 \\
42 & 78 & 65 & 73 \\
74 & 80 & 79 & 71 \\
42 & 86 & 69 & 60 \\
53 & 60 & 79 & 64 \\
50 & 59 & 64 & 66 \\
45 & 62 & 59 & 41 \\
48 & 52 & 78 & 55 \\
64 & 55 & 84 & 76 \\
38 & 50 & 60 & 62
\end{array}
$$
At the $\alpha=.05$ level of significance, test for any difference in the job satisfaction among the four professions.

Sheryl Ezze

Numerade Educator

Problem 36

Monitoring Air Pollution. The U.S. Environmental Protection Agency (EPA) monitors levels of pollutants in the air for cities across the country. Ozone pollution levels are measured using a 500 -point scale; lower scores indicate little health risk, and higher scores indicate greater health risk. The following data show the peak levels of ozone pollution in four cities (Birmingham, Alabama; Memphis, Tennessee; Little Rock, Arkansas; and Jackson, Mississippi) for 10 dates from last year.
(TABLE CAN'T COPY)
Use $\alpha=.05$ to test for any significant difference in the mean peak ozone levels among the four cities.

Shu Naito

Numerade Educator

Problem 37

College Attendance Rates. The following data show the percentage of 17 - to 24 -year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States (U.S. Census Bureau website, https $J / / \mathrm{www}$ .census.gov/data.html).
$$
\begin{array}{cccc}
\text { Northeast } & \text { Midwest } & \text { South } & \text { West } \\
28.6 & 36.7 & 59.9 & 16.4 \\
39.9 & 33.4 & 37.2 & 33.5 \\
31.9 & 22.8 & 28.0 & 22.3 \\
46.3 & 43.8 & 41.1 & 12.4 \\
32.5 & 32.1 & 33.9 & 43.7 \\
14.9 & 58.3 & 18.8 & 26.8 \\
36.8 & 31.1 & 30.3 & 57.3 \\
36.3 & 64.0 & 67.4 & 14.3 \\
37.7 & 27.6 & 32.6 & 37.0 \\
58.4 & 55.5 & 30.0 & 28.1 \\
60.6 & 78.8 & 39.1 & 17.5 \\
& 42.2 & 29.7 & 32.3 \\
& 74.7 & 29.8 & 52.4 \\
& 36.5 & 23.7 & 51.5 \\
& 28.7 & 34.0 & 25.4 \\
& 60.4 & 24.5 & 29.6 \\
& 58.2 & 54.2 & 27.6 \\
& 21.0 & 31.0 & 31.5 \\
& 28.8 & 41.9 & 22.8 \\
& 25.5 & 70.2 & 34.6 \\
& 73.9 & 22.7 & 33.0
\end{array}
$$
$$
\begin{array}{cccc}
\text { Northeast } & \text { Midwest } & \text { South } & \text { West } \\
& 36.8 & 30.7 & 37.0 \\
28.4 & 30.8 & 33.8 \\
27.2 & 21.6 & 28.7 \\
31.8 & 31.5 & 21.8 \\
& 56.8 & 38.2 & \\
28.3 & 40.2 & \\
33.3 & 35.4 & \\
39.4 & 21.6 & \\
& 39.2 & 35.5 & \\
& & 26.1 & \\
& & 32.7 &
\end{array}
$$
Use $\alpha=.05$ to test whether the mean percentage of 17 - to 24 -year-olds who are attending college is the same for the four geographic regions.

Sheryl Ezze

Numerade Educator

Problem 38

Assembly Methods. Three different assembly methods have been proposed for a new product. A completely randomized experimental design was chosen to determine which assembly method results in the greatest number of parts produced per hour, and 30 workers were randomly selected and assigned to use one of the proposed methods. The number of units produced by each worker follows.(TABLE CAN'T COPY)
Use these data and test to see whether the mean number of parts produced is the same with each method. Use $\alpha=.05$.

Sheryl Ezze

Numerade Educator

Problem 39

Job Automation. A Pew Research study conducted in 2017 found that approximately $75 \%$ of Americans believe that robots and computers might one day do many of the jobs currently done by people (Pew Research website, http//www.pewinternet .org/2017/10/04/americans-attitudes-toward-a-future-in-which-robots-and-computers -can-do-many-human-jobs/). Suppose we have the following data collected from nurses, tax auditors, and fast-food workers in which a higher score means the person feels his or her job is more likely to be automated.
$$
\begin{array}{ccc}
\text { Nurse } & \begin{array}{c}
\text { Tax } \\
\text { Auditor }
\end{array} & \begin{array}{c}
\text { Fast-Food } \\
\text { Worker }
\end{array} \\
4 & 5 & 5 \\
5 & 6 & 7 \\
6 & 5 & 5 \\
3 & 4 & 7 \\
3 & 7 & 4 \\
4 & 4 & 6 \\
5 & 6 & 5 \\
4 & 5 & 7
\end{array}
$$
a. Use $\alpha=.05$ to test for differences in the belief that a person's job is likely to be automated for the three professions.
b. Use Fisher's LSD procedure to compare the belief that a person's job will be automated for nurses and tax auditors.

Sheryl Ezze

Numerade Educator

Problem 40

Fuel Efficiency of Gasoline Brands. A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow.(TABLE CAN'T COPY)
a. At $\alpha=.05$, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline?
b. Analyze the experimental data using the ANOVA procedure for completely randomized designs. Compare your findings with those obtained in part (a). What is the advantage of attempting to remove the block effect?

Shu Naito

Numerade Educator

Problem 41

Late-Night Talk Show Viewership. Jimmy Kimmel Live! on ABC, The Tonight Show Starring Jimmy Fallon on NBC, and The Late Show with Stephen Colbert on CBS are three popular late-night talk shows. The following table shows the number of viewers in millions for a 10 -week period during the spring for each of these shows (TV by the Numbers website, https://tvbythenumbers.zap2itcom/).$$
\begin{array}{|c|c|c|c|}
\hline \text { Week } & \begin{array}{l}
\text { Jimmy Kimmel } \\
\text { Live (ABC) }
\end{array} & \begin{array}{l}
\text { The Tonight Show } \\
\text { Starring Jimmy } \\
\text { Fallon (NBC) }
\end{array} & \begin{array}{l}
\text { The Late Show with } \\
\text { Stephen Colbert (CBS) }
\end{array} \\
\hline \text { June 13-June } 17 & 2.67 & 3.24 & 2.27 \\
\hline \text { June 6-June } 10 & 2.58 & 3.32 & 2.05 \\
\hline \text { May 3D-June } 3 & 2.64 & 2.66 & 2.08 \\
\hline \text { May 23-May } 27 & 2.47 & 3.30 & 2.07 \\
\hline \text { May 16-May } 20 & 1.97 & 3.10 & 2.31 \\
\hline \text { May 9-May } 16 & 2.21 & 3.31 & 2.45 \\
\hline \text { May 2-May } 6 & 2.12 & 3.20 & 2.57 \\
\hline \text { April 25-April } 29 & 2.24 & 3.15 & 2.45 \\
\hline \text { April 18-April } 22 & 2.10 & 2.77 & 2.56 \\
\hline \text { April 11-April } 15 & 2.21 & 3.24 & 2.16 \\
\hline
\end{array}
$$
At the .05 level of significance, test for a difference in the mean number of viewers per week for the three late-night talk shows.

Shu Naito

Numerade Educator

Problem 42

Golf Club Design. A major manufacturer of golf equipment is considering three designs for a new driver: Design $A$, Design $B$, and Design $C$. Each design differs slightly in terms of the material used to construct the driver's head and shaft. The company would like to know if there is any difference in the overall driving distance for the three designs. Twelve PGA Tour players who represent the company were asked to test each model. After a warm-up period, each player hit each a drive with one of the new designs in a randomly selected order, and the overall distance (in yards) was recorded. The results follow.

$$
\begin{array}{ccc}
\text { Design A } & \text { Design B } & \text { Design C } \\
306 & 323 & 320 \\
279 & 313 & 289 \\
293 & 318 & 314 \\
277 & 288 & 282 \\
281 & 286 & 287 \\
272 & 312 & 283 \\
297 & 326 & 332 \\
271 & 306 & 284 \\
279 & 325 & 294 \\
323 & 319 & 289 \\
301 & 307 & 293
\end{array}
$$
At the .05 level of significance, test whether the mean driving distance is the same for the three designs.

Maxime Rossetti

Maxime Rossetti

Numerade Educator

Problem 43

Language Translation. A factorial experiment was designed to test for any significant differences in the time needed to translate other languages into English with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.$$
\begin{array}{lccc}
& & \text { Language } \\
& \text { Spanish } & \text { French } & \text { German } \\
\text { System 1 } & 8 & 10 & 12 \\
& 12 & 14 & 16 \\
\text { System 2 } & 6 & 14 & 16 \\
& 10 & 16 & 22
\end{array}
$$
Test for any significant differences due to language translator, type of language, and interaction. Use $\alpha=.05$.

Shu Naito

Numerade Educator

Problem 44

Defective Parts. A manufacturing company designed a factorial experiment to determine whether the number of defective parts produced by two machines differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system. The following data give the numbers of defective parts produced. Use $\alpha=.05$ to test for any significant effect due to machine, loading system, and interaction.$$
\begin{aligned}
&\text { Loading System }\\
&\begin{array}{lcc}
& \text { Manual } & \text { Automatic } \\
\text { Machine 1 } & 30 & 30 \\
& 34 & 26 \\
\text { Machine 2 } & 20 & 24 \\
& 22 & 28
\end{array}
\end{aligned}
$$

Shu Naito

Numerade Educator