7.122 List the assumptions necessary for each of the following inferential techniques:

1. a.Large-sample inferences about the difference $({\mu }_1-{\mu }_2)$ between population means, using a two-­sample z-statistic

2. b.Small-sample inferences about $({\mu }_1-{\mu }_2)$, using an independent samples design and a two-sample t-statistic

3. c.Small-sample inferences about $({\mu }_1-{\mu }_2)$, using a paired difference design and a single-sample t-statistic to analyze the differences

4. *d. Inference on comparing three treatment means, ${\mu }_1,{\mu }_2$ and ${\mu }_3$.

7.123 Independent random samples were selected from two normally distributed populations with means ${\mu }_1$ and ${\mu }_2,$ respectively. The sample sizes, means, and variances are shown in the following table:

1. Test $H_0:({\mu }_1-{\mu }_2)=0$ against $H_{\mathrm{a}}:({\mu }_1-{\mu }_2)>0.$ Use $\alpha =.05.$

2. Form a 99% confidence interval for $({\mu }_1-{\mu }_2).$

3. How large must $n_1$ and $n_2$ be if you wish to estimate $({\mu }_1-{\mu }_2)$ to within two units with 99% confidence? Assume that $n_1=n_2.$

L07124 * 7.124 An independent samples design is utilized to compare four treatment means. The data are shown in the accompanying table.

1. Given that $\mathrm{S}\mathrm{S}\mathrm{T}=36.95$ and $\text{SS}(\text{Total})=62.55,$ complete an ANOVA table for this experiment.

2. Is there evidence that the treatment means differ? Use $\alpha =.10.$

Alternate View

Treatment 1	Treatment 2	Treatment 3	Treatment 4
8	6	9	12
10	9	10	13
9	8	8	10
10	8	11	11
11	7	12	11

7.125 Two independent random samples are taken from two populations. The results of these samples are summarized in the following table:

1. Form a 90% confidence interval for $({\mu }_1-{\mu }_2).$

2. Test $H_0:({\mu }_1-{\mu }_2)=0$ against $H_a:({\mu }_1-{\mu }_2)\ne 0.$ Use $\alpha =.01.$

3. What sample size would be required if you wish to estimate $({\mu }_1-{\mu }_2)$ to within .2 with 90% confidence? Assume that $n_1=n_2.$

L07126 7.126 A random sample of five pairs of observations was selected, one observation from a population with mean ${\mu }_1,$ the other from a population with mean ${\mu }_2.$ The data are shown in the following table.

1. Test the null hypothesis $H_0:{\mu }_d=0$ against $H_{\mathrm{a}}:{\mu }_d\ne 0,$ where ${\mu }_d={\mu }_1-{\mu }_2.$ Use $\alpha =.05.$

2. Form a 95% confidence interval for ${\mu }_d.$

3. When are the procedures you used in parts a and b valid?

* 7.127 A random sample of nine pairs of observations is recorded on two variables x and y. The data are shown in the following table. Do the data provide sufficient evidence to indicate that the probability distribution for x is shifted to the right of that for y? Test, using $\alpha =.05.$

L07127 *7.128 Two independent random samples produced the measurements listed in the next table. Do the data provide sufficient evidence to conclude that there is a difference between the locations of the probability distributions for the sampled populations? Test, using $\alpha =.05.$

Alternate View

Sample 1		Sample 2
1.2	1.0	1.5	1.9
1.9	1.8	1.3	2.7
.7	1.1	2.9	3.5
2.5

7.129 Treating depression with St. John’s wort. The Journal of the American Medical Association (Apr. 18, 2001) published a study of the effectiveness of using extracts of the herbal medicine St. John’s wort in treating major depression. In an eight-week randomized, controlled trial, 200 patients diagnosed with major depression were divided into two groups, one of which $(n_1=98)$ received St. John’s wort extract while the other $(n_2=102)$ received a placebo (no drug). At the end of the study period, 14 of the St. John’s wort patients were in remission, compared with 5 of the placebo patients.

1. Compute the proportion of the St. John’s wort patients who were in remission.

2. Compute the proportion of the placebo patients who were in remission.

3. If St. John’s wort is effective in treating major depression, then the proportion of St. John’s wort patients in remission will exceed the proportion of placebo patients in remission. At $\alpha =.01,$ is St. John’s wort effective in treating major depression?

4. Repeat part c, but use $\alpha =.10.$

5. Explain why the choice of $\alpha$ is critical for this study.

CRASH 7.130 NHTSA new car crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data on new cars, saved in the CRASH file. Crash test dummies were placed in the driver’s seat and front passenger’s seat of a new car model, and the car was steered by remote control into a head-on collision with a fixed barrier while traveling at 35 miles per hour. Two of the variables measured for each of the 98 new cars in the data set are (1) the severity of the driver’s chest injury and (2) the severity of the passenger’s chest injury. (The more points assigned to the chest injury rating, the more severe the injury is.) Suppose the NHTSA wants to determine whether the true mean driver chest injury rating exceeds the true mean passenger chest injury rating and, if so, by how much.

1. State the parameter of interest to the NHTSA.

2. Explain why the data should be analyzed as matched pairs.

3. Find a 99% confidence interval for the true difference between the mean chest injury ratings of drivers and front-seat passengers.

4. Interpret the interval you found in part c. Does the true mean driver chest injury rating exceed the true mean passenger chest injury rating? If so, by how much?

5. What conditions are required for the analysis to be valid? Do these conditions hold for these data?

EVOS 7.131 Oil spill impact on seabirds. Refer to the Journal of Agricultural, Biological, and Environmental Statistics (Sept. 2000) study of the impact of a tanker oil spill on the seabird population in Alaska, presented in Exercise 2.205 (p. 111). Recall that for each of 96 shoreline locations (called transects), the number of seabirds found, the length (in kilometers) of the transect, and whether the transect was in an oiled area were recorded. (The data are saved in the EVOS file.) Observed seabird density is defined as the observed count divided by the length of the transect. A comparison of the mean densities of oiled and unoiled transects is displayed in the MINITAB printout below. Use this information to make an inference about the difference in the population mean seabird densities of oiled and unoiled transects.

MINITAB output for Exercise 7.131

7.132 Rating service at five-star hotels. A study published in the Journal of American Academy of Business, Cambridge (Mar. 2002) examined whether the perception of the quality of service at five-star hotels in Jamaica differed by gender. Hotel guests were randomly selected from the lobby and restaurant areas and asked to rate 10 service-related items (e.g., “the personal attention you received from our employees”). Each item was rated on a five-point scale $(1=“\text{much worse than I expected},”5=“\text{much better than I expected}”)$, and the sum of the items for each guest was determined. A summary of the guest scores is provided in the following table.

Alternate View

Gender	Sample Size	Mean Score	Standard Deviation
Males	127	39.08	6.73
Females	114	38.79	6.94

1. a. Construct a 90% confidence interval for the difference between the population mean service-rating scores given by male and female guests at Jamaican five-star hotels.

2. b. Use the interval you constructed in part a to make an inference about whether the perception of the quality of service at five-star hotels in Jamaica differs by gender.

3. *c. Is there evidence of a difference in the variation of guest scores for males and females? Test using $\alpha =.10.$

7.133 Effect of altitude on climbers. Dr. Philip Lieberman, a neuroscientist at Brown University, conducted a field experiment to gauge the effect of high altitude on a person’s ability to think critically. The subjects of the experiment were five males who took part in an American expedition climbing Mount Everest. At the base camp, Lieberman read sentences to the climbers while they looked at simple pictures in a book. The length of time (in seconds) it took for each climber to match the picture with a sentence was recorded. Using a radio, Lieberman repeated the task when the climbers reached a camp 5 miles above sea level. At this altitude, he noted that the climbers took 50% longer to complete the task.

1. What is the variable measured in this experiment?

2. What are the experimental units?

3. Discuss how the data should be analyzed.

*7.134 Short Message Service for cell phones. Short Message Service (SMS) is the formal name for the communication service that allows the interchange of short text messages between mobile telephone devices. Over 75% of mobile phone subscribers worldwide send or receive SMS text messages. Consequently, SMS provides an opportunity for direct marketing. In Management Dynamics (2007), marketing researchers investigated the perceptions of college students toward SMS marketing. For one portion of the study, the researchers applied the Wilcoxon rank sum test to compare the distributions of the number of text messages sent and received during peak time for two groups of cell phone users: those on an annual contract and those with a pay-as-you-go option.

1. Specify the null hypothesis tested in the words of the problem. 

2. Give the formula for the large-sample test statistic if there were 25 contract users and 40 pay-as-you-go users in the sample.

3. The Wilcoxon test results led the researchers to conclude “that contract users sent and received significantly more SMS’s during peak time than payas-you-go users.” Based on this information, draw a graph that is representative of the two SMS usage rate populations.

*7.135 College tennis recruiting with a team Web site. Most university athletic programs have a Web site with information on individual sports and a Prospective Student Athlete Form that allows high school athletes to submit information about their academic and sports achievements directly to the college coach. The Sport Journal (Winter 2004) published a study of how important team Web sites are to the recruitment of college tennis players. A survey was conducted of National Collegiate Athletic Association (NCAA) tennis coaches, of which 53 were from Division I schools, 20 were from Division II schools, and 53 were from Division III schools. Coaches were asked to respond to a series of statements, including “The Prospective Student Athlete Form on the Web site contributes very little to the recruiting process.” Responses were measured on a seven-point scale (where 1 = strongly disagree and 7 = strongly agree). In order to compare the mean responses of tennis coaches from the three NCAA divisions, the data were analyzed with an independent samples ANOVA design.

1. Identify the experimental unit, the dependent (response) variable, and the treatments in this study.

2. Give the null and alternative hypothesis for the ANOVA F-test.

3. The observed significance level of the test was found to be p-value < .003. What conclusion can you draw if you want to test at $\alpha =.05$?

7.136 Environmental impact study. Some power plants are located near rivers or oceans so that the available water can be used to cool the condensers. Suppose that, as part of an environmental impact study, a power company wants to estimate the difference in mean water temperature between the discharge of its plant and the offshore waters. How many sample measurements must be taken at each site in order to estimate the true difference between means to within .2°C with 95% confidence? Assume that the range in readings will be about 4°C at each site and that the same number of readings will be taken at each site.

7.137 Animal-assisted therapy for heart patients. Refer to the American Heart Association Conference (Nov. 2005) study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients, presented in Exercise 2.112 (p. 78). Recall that a sample of $n=26$ heart patients was visited by a human volunteer accompanied by a trained dog; the anxiety level of each patient was measured (in points) both before and after the visits. The drop (before minus after) in anxiety level for patients is summarized as follows: ${\bar{x}}_d=10.5,s_d=\mathrm{7.6.}$ Does animal-assisted therapy significantly reduce the mean anxiety level of heart failure patients? Support your answer with a 95% confidence interval.

PATENT 7.138 Patent infringement case. Chance (Fall 2002) described a lawsuit charging Intel Corp. with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the inventor of adding material to his patent notebook after the patent was witnessed and granted. The case rested on whether a patent witness’s signature was written on top of or under key text in the notebook. Intel hired a physicist who used an X-ray beam to measure the relative concentrations of certain elements (e.g., nickel, zinc, potassium) at several spots on the notebook page. The zinc measurements for three notebook locations—on a text line, on a witness line, and on the intersection of the witness and text line—are provided in the following table.

Alternate View

Text line:	.335	.374	.440
Witness line:	.210	.262	.188	.329	.439	.397
Intersection:	.393	.353	.285	.295	.319

1. a. Use a test or a confidence interval (at $\alpha =.05$ ) to compare the mean zinc measurement for the text line with the mean for the intersection.

2. b. Use a test or a confidence interval (at $\alpha =.05$ ) to compare the mean zinc measurement for the witness line with the mean for the intersection.

3. c. From the results you obtained in parts a and b, what can you infer about the mean zinc measurements at the three notebook locations?

4. *d. Conduct an ANOVA to compare the zinc measurements at the three notebook locations. Use $\alpha =.05$.

5. *e. Use a nonparametric test (at $\alpha =.05$ ) to compare the distribution of zinc measurements for the text line with the corresponding distribution for the intersection.

6. *f. Use a nonparametric test (at $\alpha =.05$ ) to compare the distribution of zinc measurements for the witness line with the corresponding distribution for the intersection.

7.139 Reading tongue twisters. According to Webster’s New World Dictionary, a tongue twister is “a phrase that is hard to speak rapidly.” Do tongue twisters have an effect on the length of time it takes to read silently? To answer this question, 42 undergraduate psychology students participated in a reading experiment (Memory & Cognition, Sept. 1997). Two lists, each composed of 600 words, were constructed. One list contained a series of tongue twisters, and the other list (called the control) did not contain any tongue twisters. Each student read both lists, and the length of time (in minutes) required to complete the lists was recorded. The researchers used a test of hypothesis to compare the mean reading response times for the tongue-twister and control lists.

1. Set up the null hypothesis for the test.

2. For each student, the researchers computed the difference between the reading response times for the tongue-twister and control lists. The mean difference was .25 minute with a standard deviation of .78 minute. Use the information to find the test statistic and p-value of the test.

3. Give the appropriate conclusion. Use $\alpha =.05.$

ANTS 7.140 Mongolian desert ants. Refer to the Journal of Biogeography (Dec. 2003) study of ants in Mongolia (central Asia), presented in Exercise 2.68 (p. 63). Recall that botanists placed seed baits at 5 sites in the Dry Steppe region and 6 sites in the Gobi Desert and observed the number of ant species attracted to each site. These data are listed in the next table.

1. Is there evidence to conclude that a difference exists between the average number of ant species found at sites in the two regions of Mongolia? Draw the appropriate conclusion, using $\alpha =.05.$

2. Conduct a test of equal variances at the two regions, using $\alpha =.05$. Interpret the result.

TWINS 7.141 Identical twins reared apart. Because they share an identical genotype, twins make ideal subjects for investigating the degree to which various environmental conditions affect personality. The classical method of studying this phenomenon, and the subject of a book by Susan Farber (Identical Twins Reared Apart, New York: Basic Books, 1981), is the study of identical twins separated early in life and reared apart. Much of Farber’s discussion focuses on a comparison of IQ scores. The data for this analysis appear in the accompanying table. One member (A) of each of the $n=32$ pairs of twins was reared by a natural parent; the other member (B) was reared by a relative or some other person.

1. a. Is there a significant difference between the average IQ scores of identical twins when one member of the pair is reared by the natural parents and the other member of the pair is not? Use $\alpha =.05$ to draw your conclusion.

2. *b. Analyze the data using a nonparametric test at $\alpha =.05.$ Does the result agree with the result, part a?

GENES 7.142 Light-to-dark transition of genes. Synechocystis, a type of bacterium that can grow and survive under a wide range of conditions, is used by scientists to model DNA behavior. In the Journal of Bacteriology (July 2002), scientists isolated genes of the bacterium responsible for photosynthesis and respiration and investigated the sensitivity of the genes to light. Each gene sample was grown in an incubator in “full light.” The lights were then extinguished, and any growth of the sample was measured after 24 hours in the dark (“full dark”). The lights were then turned back on for 90 minutes (“transient light”), followed immediately by an additional 90 minutes in the dark (“transient dark”). Standardized growth measurements in each light–dark condition were obtained for 103 genes. The complete data set is saved in the GENES file. Data on the first 10 genes are shown in the following table.

1. a. Treat the data for the first 10 genes as a random sample collected from the population of 103 genes, and test the hypothesis that there is no difference between the mean standardized growth of genes in the full-dark condition and genes in the transient-light condition. Use $\alpha =.01.$

2. b. Use a statistical software package to compute the mean difference in standardized growth of the 103 genes in the full-dark condition and the transient-light condition. Did the test you carried out in part a detect this difference?

3. c. Repeat parts a and b for a comparison of the mean standardized growth of genes in the full-dark condition and genes in the transient-dark condition.

4. d. Repeat parts a and b for a comparison of the mean standardized growth of genes in the transient-light condition and genes in the transient-dark condition.

5. *e. Using data for the first 10 genes, run an ANOVA to compare the means at the three conditions. Use $\alpha =.01.$

7.143 Pig castration study. Two methods of castrating male piglets were investigated in Applied Animal Behaviour Science (Nov. 1, 2000). Method 1 involved an incision in the spermatic cords, while Method 2 involved pulling and severing the cords. Forty-nine male piglets were randomly allocated to one of the two methods. During castration, the researchers measured the number of high-frequency vocal responses (squeals) per second over a 5-second period. The data are summarized in the accompanying table. Conduct a test of hypothesis to determine whether the population mean number of high-frequency vocal responses differs for piglets castrated by the two methods. Use $\alpha =.05.$

RATPUPS 7.144 Swim maze study. Merck Research Labs used the single-T swim maze to conduct an experiment to evaluate the effect of a new drug. Nineteen impregnated dam rats were allocated a dosage of 12.5 milligrams of the drug. One male and one female rat pup were randomly selected from each resulting litter to perform in the swim maze. Each pup was placed in the water at one end of the maze and allowed to swim until it escaped at the opposite end. If the pup failed to escape after a certain period of time, it was placed at the beginning of the maze and given another chance. The experiment was repeated until each pup accomplished three successful escapes. The accompanying table reports the number of swims required by each pup to perform three successful escapes. Is there sufficient evidence of a difference between the mean number of swims required by male and female pups? Conduct the test (at $\alpha =.10$ ). Comment on the assumptions required for the test to be valid.

CIRCUIT 7.145 Testing electronic circuits. Japanese researchers have developed a compression–depression method of testing electronic circuits based on Huffman coding (IEICE Transactions on Information & Systems, Jan. 2005). The new method is designed to reduce the time required for input decompression and output compression—called the compression ratio. Experimental results were obtained by testing a sample of 11 benchmark circuits (all of different sizes) from a SUN Blade 1000 workstation. Each circuit was tested with the standard compression–depression method and the new Huffman-based coding method and the compression ratio recorded. The data are given in the next table.

1. Compare the two methods with a 95% confidence interval. Which method has the smaller mean compression ratio?

2. How many circuits need to be sampled in order to estimate the mean difference in compression ratio to within .03 with 95% confidence.

7.147 SMWT Self-managed work teams and family life. To improve quality, productivity, and timeliness, more and more American industries are utilizing self-managed work teams (SMWTs). A team typically consists of 5 to 15 workers who are collectively responsible for making decisions and performing all tasks related to a particular project. Researchers L. Stanley-Stevens (Tarleton State University), D. E. Yeatts, and R. R. Seward (both from the University of North Texas) investigated the connection between SMWTs, work characteristics, and workers’ perceptions of positive spillover into family life (Quality Management Journal, Summer 1995). Survey data were collected from 114 AT&T employees who worked on 1 of 15 SMWTs at an AT&T technical division. The workers were divided into two groups: (1) those who reported a positive spillover of work skills to family life and (2) those who did not report any such positive work spillover. The two groups were compared on a variety of job and demographic characteristics, several of which are shown in the table (next column). All but the demographic characteristics were measured on a seven-point scale, ranging from $1=$ “strongly disagree” to $7=$ “strongly agree”; thus, the larger the number, the more the characteristic was indicated. The file named SMWT includes the values of the variables listed in the table for each of the 114 survey participants. The researchers’ objectives were to compare the two groups of workers on each characteristic. In particular, they wanted to know which job-related characteristics are most highly associated with positive work spillover. Conduct a complete analysis of the data for the researchers.