Problem 7
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. 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. Reducing Errors in Grammar A composition teacher wishes to see whether a new smartphone app will reduce the number of grammatical errors her students make when writing a two-page essay. She randomly selects six students, and the data are shown. At \(\alpha=0.025\) can it be concluded that the number of errors has been reduced? $$ \begin{array}{l|cccccc}{\text { Student }} & {1} & {2} & {3} & {4} & {5} & {6} \\\ \hline \text { Errors before } & {12} & {9} & {0} & {5} & {4} & {3} \\\ \hline \text { Errors after } & {9} & {6} & {1} & {3} & {2} & {3}\end{array} $$
Problem 7
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. Lecture versus Computer-Assisted Instruction A survey found that \(83 \%\) of the men questioned preferred computer-assisted instruction to lecture and \(75 \%\) of the women preferred computer-assisted instruction to lecture. There were 100 randomly selected individuals in each sample. At \(\alpha=0.05\) test the claim that there is no difference in the proportion of men and the proportion of women who favor computer-assisted instruction over lecture. Find the \(95 \%\) confidence interval for the difference of the two proportions.
Problem 7
Weights of Running Shoes The weights in ounces of a sample of running shoes for men and women are shown. Test the claim that the means are different. Use the \(P\) -value method with \(\alpha=0.05 .\) $$ \begin{array}{ll|ccc}{\text { Men }} & {} & {\text { Women }} & {} \\ \hline 10.4 & {12.6} & {10.6} & {10.2} & {8.8} \\ {1.1} & {14.7} & {9.6} & {9.5} & {9.5} \\ {10.8} & {12.9} & {10.1} & {11.2} & {9.3} \\ {11.7} & {13.3} & {9.4} & {10.3} & {9.5} \\ {12.8} & {14.5} & {9.8} & {10.3} & {11.0} \\\ \hline\end{array} $$
Problem 7
Commuting Times The U.S. Census Bureau reports that the average commuting time for citizens of both Baltimore, Maryland, and Miami, Florida, is approximately 29 minutes. To see if their commuting times appear to be any different in the winter, random samples of 40 drivers were surveyed in each city and the average commuting time for the month of January was calculated for both cities. The results are shown. At the 0.05 level of significance, can it be concluded that the commuting times are different in the winter? $$ \begin{array}{lcc}{} & {\text { Miami }} & {\text { Baltimore }} \\ \hline \text { Sample size } & {40} & {40} \\ {\text { Sample mean }} & {28.5 \min } & {35.2 \mathrm{min}} \\ {\text { Population standard deviation }} & {7.2 \mathrm{min}} & {9.1 \mathrm{min}}\end{array} $$
Problem 8
Teacher Salaries A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers in a large school district. The mean of the salaries of a random sample of 26 elementary school teachers is dollar 48,256, and the sample standard deviation is dollar 3,912.40 . The mean of the salaries of a random sample of 24 secondary school teachers is dollar 45,633 . The sample standard deviation is dollar 5533 . At \(\alpha=0.05,\) can it be concluded that the mean of the salaries of the elementary school teachers is greater than the mean of the salaries of the secondary school teachers? Use the \(P\) -value method.
Problem 8
Heights of 9 -Year-Olds At age 9 the average weight \((21.3 \mathrm{kg})\) and the average height \((124.5 \mathrm{cm})\) for both boys and girls are exactly the same. A random sample of 9 -year-olds yielded these results. At \(\alpha=0.05,\) do the data support the given claim that there is a difference in heights? $$ \begin{array}{lcc}{} & {\text { Boys }} & {\text { Girls }} \\ \hline \text { Sample size } & {60} & {50} \\ {\text { Mean height, } \mathrm{cm}} & {123.5} & {126.2} \\ {\text { Population variance }} & {98} & {120}\end{array} $$
Problem 8
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. 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. Overweight Dogs A veterinary nutritionist developed a diet for overweight dogs. The total volume of food consumed remains the same, but one-half of the dog food is replaced with a low-calorie "filler" such as canned green beans. Six overweight dogs were randomly selected from her practice and were put on this program. Their initial weights were recorded, and they were weighed again after 4 weeks. At the 0.05 level of significance, can it be concluded that the dogs lost weight? $$ \begin{array}{l|cccccc}{\text { Before }} & {42} & {53} & {48} & {65} & {40} & {52} \\ \hline \text { After } & {39} & {45} & {40} & {58} & {42} & {47}\end{array} $$
Problem 8
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. Leisure Time In a sample of \(150 \mathrm{men}, 132\) said that they had less leisure time today than they had 10 years ago. In a random sample of 250 women, 240 women said that they had less leisure time than they had 10 years ago. At \(\alpha=0.10,\) is there a difference in the proportions? Find the \(90 \%\) confidence interval for the difference of the two proportions. Does the confidence interval contain \(0 ?\) Give a reason why this information would be of interest to a researcher.
Problem 9
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. Wolf Pack Pups Does the variance in the number of pups per pack differ between Montana and Idaho wolf packs? Random samples of packs were selected for each area, and the numbers of pups per pack were recorded. At the 0.05 level of significance, can a difference in variances be concluded? $$ \begin{array}{l|cccccccc}{\text { Montana }} & {4} & {3} & {5} & {6} & {1} & {2} & {8} & {2} \\ \hline \text { wolf packs } & {3} & {1} & {7} & {6} & {5} & {} & {} \\ \hline \text { Idaho } & {2} & {4} & {5} & {4} & {2} & {4} & {6} & {3} \\ \hline \text { wolf packs } & {1} & {4} & {2} & {1} & {}\end{array} $$
Problem 9
For Exercises 2 through \(12,\) perform each of these steps. Assume that all variables are normally or approximately normally distributed. 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. Pulse Rates of Identical Twins A researcher wanted to compare the pulse rates of identical twins to see whether there was any difference. Eight sets of twins were randomly selected. The rates are given in the table as number of beats per minute. At \(\alpha=0.01,\) is there a significant difference in the average pulse rates of twins? Use the \(P\) -value method. Find the \(99 \%\) confidence interval for the difference of the two. $$ \begin{array}{l|cccccccc}{\text { Twin } \mathbf{A}} & {87} & {92} & {78} & {83} & {88} & {90} & {84} & {93} \\ \hline \text { Twin B } & {83} & {95} & {79} & {83} & {86} & {93} & {80} & {86}\end{array} $$
