Problem 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. Cyber School Enrollments Shown are the numbers of students enrolled in cyber school for five randomly selected school districts and the per-pupil costs for the cyber school education. At \(\alpha=0.10\), is there a relationship between the two variables? How might this information be useful to school administrators? $$ \begin{array}{l|ccccc} \text { Number of students } & 10 & 6 & 17 & 8 & 11 \\ \hline \text { Per-pupil cost } & 7200 & 9393 & 7385 & 4500 & 8203 \end{array} $$
Problem 13
A researcher wishes to compare the prices for randomly selected prescription drugs in the United States with those in Canada. The same drugs and dosages were compared in each country. At \(\alpha=0.05,\) can it be concluded that the drugs in Canada are cheaper? $$ \begin{array}{l|cccccc} \text { Drug } & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { United States } & 3.31 & 2.27 & 2.54 & 3.13 & 23.40 & 3.16 \\ \hline \text { Canada } & 1.47 & 1.07 & 1.34 & 1.34 & 21.44 & 1.47 \end{array} $$ $$ \begin{array}{l|cccc} \text { Drug } & 7 & 8 & 9 & 10 \\ \hline \text { United States } & 1.98 & 5.27 & 1.96 & 1.11 \\ \hline \text { Canada } & 1.07 & 3.39 & 2.22 & 1.13 \end{array} $$
Problem 14
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. Drug Prices Shown are the price for a human dose of several randomly selected prescription drugs and the price for an equivalent dose for animals. At \(\alpha=0.10\), is there a relationship between the variables? $$ \begin{array}{l|llllllll} \text { Humans } & 0.67 & 0.64 & 1.20 & 0.51 & 0.87 & 0.74 & 0.50 & 1.22 \\ \hline \text { Animals } & 0.13 & 0.18 & 0.42 & 0.25 & 0.57 & 0.58 & 0.49 & 1.28 \end{array} $$
Problem 15
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. A study was conducted to see if a set of exercises would reduce the number of times a person visits a physical therapist. Eight subjects were selected, and the number of times over a threemonth period that they visited a physical therapist was recorded. They were then given the exercise program, and the number of times they visited a physical therapist was recorded. The data are shown. At \(\alpha=0.05\) can you conclude that the exercise program was effective; that is, did it reduce the number of times a person visited the physical therapist? $$ \begin{array}{l|rrrrrrrr} \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } \\ \hline \text { Visits before } & 12 & 15 & 9 & 10 & 11 & 5 & 9 & 7 \\ \hline \text { Visits after } & 8 & 13 & 10 & 7 & 6 & 8 & 3 & 4 \end{array} $$
Problem 15
Cavities in Fourth-Grade Students A school dentist wanted to test the claim, at \(\alpha=0.05,\) that the number of cavities in fourth-grade students is random. Forty students were checked, and the number of cavities each had is shown here. Test for randomness of the values above or below the median. $$ \begin{array}{lllllllllll} 0 & 4 & 6 & 0 & 6 & 2 & 5 & 3 & 1 & 5 & 1 \\ 2 & 2 & 1 & 3 & 7 & 3 & 6 & 0 & 2 & 6 & 0 \\ 2 & 3 & 1 & 5 & 2 & 1 & 3 & 0 & 2 & 3 & 7 \\ 3 & 1 & 5 & 1 & 1 & 2 & 2 & & & & \end{array} $$
Problem 16
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. A statistics professor wants to investigate the relationship between a student's midterm examination score and the score on the final. Eight students were randomly selected, and their scores on the two examinations are noted. At the 0.10 level of significance, is there sufficient evidence to conclude that there is a difference in scores? $$ \begin{array}{l|rrrrrrrr} \text { Student } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline \text { Midterm } & 75 & 92 & 68 & 85 & 65 & 80 & 75 & 80 \\ \hline \text { Final } & 82 & 90 & 79 & 95 & 70 & 83 & 72 & 79 \end{array} $$
Problem 16
Daily Lottery Numbers Listed below are the daily numbers (daytime drawing) for the Pennsylvania State Lottery for February 2007. Using O for odd and E for even, test for randomness at \(\alpha=0.05\). $$\begin{array}{lllllll}270 & 054 & 373 & 204 & 908 & 121 & 121 \\ 804 & 116 & 467 & 357 & 926 & 626 & 247 \\\ 783 & 554 & 406 & 272 & 508 & 764 & 890 \\ 441 & 964 & 606 & 568 & 039 & 370 & 583\end{array}$$
Problem 17
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. Ten college students were selected and asked how many soft drinks they drink over a twoweek period. These students were asked to replace some of the soft drinks with water in order to cut down on the amount of soft drinks that they consumed. At \(\alpha=0.10,\) was there a decrease in the amount of soft drinks consumed over a two-week period? The results are shown. $$ \begin{array}{l|cccccccccc} \text { Student } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } & \text { F } & \text { G } & \text { H } & \text { I } & \text { J } \\ \hline \text { Before } & 6 & 12 & 15 & 20 & 18 & 24 & 9 & 7 & 26 & 21 \\ \hline \text { After } & 8 & 10 & 12 & 17 & 14 & 21 & 11 & 8 & 23 & 17 \end{array} $$
Problem 18
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. A researcher wishes to test the effects of a pill on a person's appetite. Twelve randomly selected subjects are allowed to eat a meal of their choice, and their caloric intake is measured. The next day, the same subjects take the pill and eat a meal of their choice. The caloric intake of the second meal is measured. The data are shown here. At \(\alpha=0.02,\) can the researcher conclude that the pill had an effect on a person's appetite? $$ \begin{array}{l|ccccccc} \text { Subject } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \text { Meal 1 } & 856 & 732 & 900 & 1321 & 843 & 642 & 738 \\ \hline \text { Meal 2 } & 843 & 721 & 872 & 1341 & 805 & 531 & 740 \end{array} $$ $$ \begin{array}{l|rrrrr} \text { Subject } & 8 & 9 & 10 & 11 & 12 \\ \hline \text { Meal 1 } & 1005 & 888 & 756 & 911 & 998 \\ \hline \text { Meal 2 } & 900 & 805 & 695 & 878 & 914 \end{array} $$
Problem 18
Random Numbers Random? A calculator generated these integers randomly. Apply the runs test to see if you can reject the hypothesis that the numbers are truly random. Use \(\alpha=0.05 .\) $$ \begin{array}{lllllllllll} 1 & 1 & 1 & 1 & 1 & 1 & 2 & 1 & 1 & 1 & 1 \\ 2 & 2 & 1 & 2 & 1 & 2 & 2 & 1 & 2 & 1 & 1 \\ 2 & 1 & 1 & & & & & & & & \end{array} $$
