Chapter 9

Working Breath Rate Two random samples of 32 individuals were selected. One sample participated in an activity which simulates hard work. The average breath rate of these individuals was 21 breaths per minute. The other sample did some normal walking. The mean breath rate of these individuals was 14. Find the 90 \(\%\) confidence interval of the difference in the breath rates if the population standard deviation was 4.2 for breath rate per minute.

Traveling Distances Find the \(95 \%\) confidence interval of the difference in the distance that day students travel to school and the distance evening students travel to school. Two random samples of 40 students are taken, and the data are shown. Find the \(95 \%\) confidence interval of the difference in the means. $$ \begin{array}{lccc}{} & {\bar{X}} & {\sigma} & {n} \\ \hline \text { Day students } & {4.7} & {1.5} & {40} \\ {\text { Evening Students }} & {6.2} & {1.7} & {40}\end{array} $$

For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Airlines On-Time Arrivals The percentages of on-time arrivals for major U.S. airlines range from 68.6 to 91.1. Two regional airlines were surveyed with the following results. At \(\alpha=0.01,\) is there a difference in proportions? $$ \begin{array}{ccc}{} & {\text { Airline } \mathbf{A}} & {\text { Airline } \mathbf{B}} \\ \hline \text { No.of flights } & {300} & {250} \\ {\text { No. of on-time flights }} & {213} & {185}\end{array} $$

For Exercises 9 through \(24,\) perform the following steps. Assume that all variables are normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Reading Program Summer reading programs are very popular with children. At the Citizens Library, Team Ramona read an average of 23.2 books with a standard deviation of \(6.1 .\) There were 21 members on this team. Team Beezus read an average of 26.1 books with a standard deviation of \(2.3 .\) There 23 members on this team. Did the variances of the two teams differ? Use \(\alpha=0.05 .\)

Gasoline Prices A random sample of monthly gasoline prices was taken from 2011 and from 2015. The samples are shown. Using \(\alpha=0.01,\) can it be concluded that gasoline cost more in 2015? Use the \(P\) -value method. $$ \frac{2011}{2015} | \begin{array}{cccccc}{2011} & {2.02} & {2.47} & {2.50} & {2.70} & {3.13} & {2.56} \\ \hline 2015 & {2.36} & {2.46} & {2.63} & {2.76} & {3.00} & {2.85} & {2.77}\end{array} $$

Age Differences In a large hospital, a nursing director selected a random sample of 30 registered nurses and found that the mean of their ages was \(30.2 .\) The population standard deviation for the ages is \(5.6 .\) She selected a random sample of 40 nursing assistants and found the mean of their ages was \(31.7 .\) The population standard deviation of the ages for the assistants is \(4.3 .\) Find the \(99 \%\) confidence interval of the differences in the ages.

For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Married People In a specific year \(53.7 \%\) of men in the United States were married and \(50.3 \%\) of women were married. Two independent random samples of 300 men and 300 women found that 178 men and 139 women were married (not to each other). At the 0.05 level of significance, can it be concluded that the proportion of men who were married is greater than the proportion of women who were married?

For Exercises 9 through \(24,\) perform the following steps. Assume that all variables are normally distributed. a. State the hypotheses and identify the claim. b. Find the critical value. c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. School Teachers' Salaries A researcher claims that the variation in the salaries of elementary school teachers is greater than the variation in the salaries of secondary school teachers. A random sample of the salaries of 30 elementary school teachers has a variance of \(8324,\) and a random sample of the salaries of 30 secondary school teachers has a variance of \(2862 .\) At \(\alpha=0.05\) can the researcher conclude that the variation in the elementary school teachers' salaries is greater than the variation in the secondary school teachers' salaries? Use the \(P\) -value method.

Miniature Golf Scores A large group of friends went miniature golfing together at a par 54 course and decided to play on two teams. A random sample of scores from each of the two teams is shown. At \(\alpha=0.05\) is there a difference in mean scores between the two teams? Use the \(P\) -value method. $$ \begin{array}{l|lllllll}{\text { Team } 1} & {61} & {44} & {52} & {47} & {56} & {63} & {62} & {55} \\ \hline \text { Team 2} & {56} & {40} & {42} & {58} & {48} & {52} & {51}\end{array} $$

For Exercises 7 through \(27,\) perform these steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Undergraduate Financial Aid A study is conducted to determine if the percent of women who receive financial aid in undergraduate school is different from the percent of men who receive financial aid in undergraduate school. A random sample of undergraduates revealed these results. At \(\alpha=0.01,\) is there significant evidence to reject the null hypothesis? $$ \begin{array}{ll}\hline & {\text { Women } \quad \text { Men }} \\ \hline \text { Sample size } & {250} & {300} \\ {\text { Number receiving aid }} & {200} & {180}\end{array} $$