Chapter 13

Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use \(\alpha=0.05\). d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Mathematics Achievement Test Scores The National Assessment of Educational Progress (U.S. Department of Education) tests mathematics, reading, and science achievement in grades 4 and 8 . A random sample of states is selected, and their mathematics achievement scores are noted for fourth- and eighth- graders. At \(\alpha=0.05,\) can a linear relationship be concluded between the data? $$ \begin{array}{l|rrrrrrr} \text { Grade } \mathbf{4} & 90 & 84 & 80 & 87 & 88 & 77 & 79 \\ \hline \text { Grade } \mathbf{8} & 81 & 75 & 66 & 76 & 80 & 59 & 74 \end{array} $$

Explain what is meant by the efficiency of a nonparametric test.

Use the Kruskal-Wallis test and perform these steps. 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. Job Offers for Chemical Engineers A recent study recorded the number of job offers received by randomly selected, newly graduated chemical engineers at three colleges. The data are shown here. At \(\alpha=0.05,\) is there a difference in the average number of job offers received by the graduates at the three colleges? $$ \begin{array}{ccc} \text { College A } & \text { College B } & \text { College C } \\ \hline 6 & 2 & 10 \\ 8 & 1 & 12 \\ 7 & 0 & 9 \\ 5 & 3 & 13 \\ 6 & 6 & 4 \end{array} $$

Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use \(\alpha=0.05\). d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Subway and Commuter Rail Passengers Six cities are randomly selected, and the number of daily passenger trips (in thousands) for subways and commuter rail service is obtained. At \(\alpha=0.05,\) is there a relationship between the variables? Suggest one reason why the transportation authority might use the results of this study. $$ \begin{array}{l|rrrrrr} \text { City } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Subway } & 845 & 494 & 425 & 313 & 108 & 41 \\ \hline \text { Rail } & 39 & 291 & 142 & 103 & 33 & 38 \end{array} $$

To test the claim that there is no difference in the lifetimes of two brands of handheld video games, a researcher selects a random sample of 11 video games of each brand. The lifetimes (in months) of each brand are shown. At \(\alpha=0.01\), can the researcher conclude that there is a difference in the distributions of lifetimes for the two brands? $$\begin{array}{l|ccccccccccc}\text { Brand A } & 42 & 34 & 39 & 42 & 22 & 47 & 51 & 34 & 41 & 39 & 28 \\\\\hline \text { Brand B } & 29 & 39 & 38 & 43 & 45 & 49 & 53 & 38 & 44 & 43 & 32\end{array}$$

For Exercises 5 through \(20,\) 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. The U.S. median annual income for men in 2014 (in constant dollars) was \(\$ 35,642 .\) A random sample of recent male college graduates indicated the following incomes. At the 0.05 level of significance, test the claim that the median is more than \(\$ 35,642\) $$ \begin{array}{lllll} 35,000 & 37,682 & 39,800 & 32,500 & 30,000 \\ 41,050 & 36,198 & 31,500 & 29,650 & 35,800 \\ 34,500 & 38,850 & 39,750 & & \end{array} $$

Use the Kruskal-Wallis test and perform these steps. 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. Expenditures for Pupils The expenditures in dollars per pupil for randomly selected states in three sections of the country are listed below. At \(\alpha=0.05,\) can it be concluded that there is a difference in spending between regions? $$ \begin{array}{ccc} \text { Eastern third } & \text { Middle third } & \text { Western third } \\ \hline 6701 & 9854 & 7584 \\ 6708 & 8414 & 5474 \\ 9186 & 7279 & 6622 \\ 6786 & 7311 & 9673 \\ 9261 & 6947 & 7353 \end{array} $$

Stopping Distances of Automobiles A researcher wishes to see if the stopping distance for midsize automobiles is different from the stopping distance for compact automobiles at a speed of 70 miles per hour. The data are shown for two random samples. At \(\alpha=0.10,\) test the claim that the stopping distances are the same. If one of your safety concerns is stopping distance, will it make a difference which type of automobile you purchase? $$\begin{array}{l|cccccccccc}\text { Automobile } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\\\\hline \text { Midsize } & 188 & 190 & 195 & 192 & 186 & 194 & 188 & 187 & 214 & 203 \\\\\hline \text { Compact } & 200 & 211 & 206 & 297 & 198 & 204 & 218 & 212 & 196 & 193\end{array}$$

Rank each set of data. $$ 25,68,36,63,36,74,39 $$

Perform these steps. a. Find the Spearman rank correlation coefficient. b. State the hypotheses. c. Find the critical value. Use \(\alpha=0.05\). d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. Motion Picture Releases and Gross Revenue In Chapter 10 it was demonstrated that there was a significant linear relationship between the numbers of releases that a motion picture studio put out and its gross receipts for the year. Is there a relationship between the two at the 0.05 level of significance? $$ \begin{array}{l|ccccccccc} \begin{array}{l} \text { No. of } \\ \text { releases } \end{array} & 361 & 270 & 306 & 22 & 35 & 10 & 8 & 12 & 21 \\ \hline \text { Receipts } & 2844 & 1967 & 1371 & 1064 & 667 & 241 & 188 & 154 & 125 \end{array} $$