Problem 9
Length of Hospital Stays The average length of "short hospital stays" for men is slightly longer than that for women, 5.2 days versus 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At \(\alpha=0.01,\) is there sufficient evidence to conclude that the average hospital stay for men is longer than the average hospital stay for women? $$ \begin{array}{lcc}{} & {\text { Men }} & {\text { Women }} \\ \hline \text { Sample size } & {32} & {30} \\ {\text { Sample mean }} & {5.5 \text { days }} & {4.2 \text { days }} \\ {\text { Population standard deviation }} & {1.2 \text { days }} & {1.5 \text { days }}\end{array} $$
Problem 10
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. Animal Bites of Postal Workers In Cleveland, a random sample of 73 mail carriers showed that 10 had been bitten by an animal during one week. In Philadelphia, in a random sample of 80 mail carriers, 16 had received animal bites. Is there a significant difference in the proportions? Use \(\alpha=0.05 .\) Find the \(95 \%\) confidence interval for the difference of the two proportions.
Problem 10
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. Toy Assembly Test An educational researcher devised a wooden toy assembly project to test learning in 6-year-olds. The time in seconds to assemble the project was noted, and the toy was disassembled out of the child's sight. Then the child was given the task to repeat. The researcher would conclude that learning occurred if the mean of the second assembly times was less than the mean of the first assembly times. At \(\alpha=0.01,\) can it be concluded that learning took place? Use the \(P\) -value method, and find the \(99 \%\) confidence interval of the difference in means. $$ \begin{array}{l|ccccccc}{\text { Child }} & {1} & {2} & {3} & {4} & {5} & {6} & {7} \\ \hline \text { Trial } 1 & {100} & {150} & {150} & {110} & {130} & {120} & {118} \\ \hline \text { Trial 2} & {90} & {130} & {150} & {90} & {105} & {110} & {120}\end{array} $$
Problem 10
Home Prices A real estate agent compares the selling prices of randomly selected homes in two municipalities in southwestern Pennsylvania to see if there is a difference. The results of the study are shown. Is there enough evidence to reject the claim that the average cost of a home in both locations is the same? Use \(\alpha=0.01 .\) $$ \begin{array}{cc}{\text { Scott }} & {\text { Ligonier }} \\ \hline \overline{X_{1}=\$ 93,430^{*}} & {\bar{X}_{2}=\$ 98,043^{*}} \\\ {\sigma_{1}=\$ 5602} & {\sigma_{2}=\$ 4731} \\ {n_{1}=35} & {n_{2}=40}\end{array} $$
Problem 10
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. Noise Levels in Hospitals In a hospital study, it was found that the standard deviation of the sound levels from 20 randomly selected areas designated as "casualty doors" "was 4.1 dB A and the standard deviation of 24 randomly selected areas designated as operating theaters was 7.5 dB A. At \(\alpha=0.05,\) can you substantiate the claim that there is a difference in the standard deviations?
Problem 11
Manual Dexterity Differences A researcher wishes to see if there is a difference in the manual dexterity of athletes and that of band members. Two random samples of 30 are selected from each group and are given a manual dexterity test. The mean of the athletes test was \(87,\) and the mean of the band members' test was \(92 .\) The population standard deviation for the test is \(7.2 .\) At \(\alpha=0.01,\) is there a significant difference in the mean scores?
Problem 11
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 Spelling A ninth-grade teacher wishes to see if a new spelling program will reduce the spelling errors in his students' writing. The number of spelling errors made by the students in a five-page report before the program is shown. Then the number of spelling errors made by students in a five-page report after the program is shown. At \(\alpha=0.05,\) did the program work? $$ \begin{array}{lllllll}{\text { Before }} & {8} & {3} & {10} & {5} & {9} & {11} & {12} \\ \hline \text { After } & {6} & {4} & {8} & {1} & {4} & {7} & {11}\end{array} $$
Problem 11
Hours Spent Watching Television According to Nielsen Media Research, children (ages 2-11) spend an average of 21 hours 30 minutes watching television per week while teens (ages 12-17) spend an average of 20 hours 40 minutes. Based on the sample statistics shown, is there sufficient evidence to conclude a difference in average television watching times between the two groups? Use \(\alpha=0.01 .\) $$ \begin{array}{lcc}{} & {\text { Children }} & {\text { Teens }} \\ \hline \text { Sample mean } & {22.45} & {18.50} \\ {\text { Sample variance }} & {16.4} & {18.2} \\ {\text { Sample size }} & {15} & {15}\end{array} $$
Problem 12
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. Winter Temperatures A random sample of daily high temperatures in January and February is listed. At \(\alpha=0.05,\) can it be concluded that there is a difference in variances in high temperature between the two months? $$ \begin{array}{l|ccccccccccc}{\text { Jan. }} & {31} & {31} & {38} & {24} & {24} & {42} & {22} & {43} & {35} & {42} \\ \hline \text { Feb. } & {31} & {29} & {24} & {30} & {28} & {24} & {27} & {34} & {27}\end{array} $$
Problem 12
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. Mistakes in a Song A random sample of six music students played a short song, and the number of mistakes in music each student made was recorded. After they practiced the song 5 times, the number of mistakes each student made was recorded. The data are shown. At \(\alpha=0.05,\) can it be concluded that there was a decrease in the mean number of mistakes? $$ \begin{array}{l|cccccc}{\text { Student }} & {\mathrm{A}} & {\mathrm{B}} & {\mathrm{C}} & {\mathrm{D}} & {\mathrm{E}} & {\mathrm{F}} \\ \hline \text { Before } & {10} & {6} & {8} & {8} & {13} & {8} \\ \hline \text { After } & {4} & {2} & {2} & {7} & {8} & {9}\end{array} $$
