Problem 3
List the advantages of nonparametric statistics.
Problem 3
The 2014 women's 1000 -meter speed skating winning time was \(1: 14: 02,\) posted by Zhang Hong of China. In preparation for the 2018 Winter Olympics in Pyeongchang, South Korea several randomly selected students from two different universities posted the following times (rounded to the nearest second). Test the claim that there is no difference in times between universities at $\alpha=0.05 .$$$\begin{array}{l|llllllllll}\text { UA } & 2: 05 & 2: 15 & 1: 58 & 1: 42 & 2: 01 & 1: 40 & 1: 39 & 2: 20 & 1: 51 & 2: 03 \\ \hline \text { UB } & 2: 10 & 2: 06 & 1: 35 & 1: 48 & 1: 38 & 2: 00 & 2: 15 & 2: 14 & 2: 27 & 1: 48\end{array}$$
Problem 4
When \(n>25\), what is used in place of Table J for the sign test?
Problem 4
List the disadvantages of nonparametric statistics.
Problem 4
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. Sodium Content of Microwave Dinners Three brands of microwave dinners were advertised as low in sodium. Random samples of the three different brands show the following milligrams of sodium. At \(\alpha=0.05,\) is there a difference in the amount of sodium among the brands? $$ \begin{array}{ccc} \text { Brand A } & \text { Brand B } & \text { Brand C } \\ \hline 810 & 917 & 893 \\ 702 & 912 & 790 \\ 853 & 952 & 603 \\ 703 & 958 & 744 \\ 892 & 893 & 623 \\ 732 & & 743 \\ 713 & & 609 \\ 613 & & \end{array} $$
Problem 4
Find the sum of the signed ranks. Assume that the samples are dependent. State which sum is used as the test value. $$ \begin{array}{l|llllllll} \text { Pretest } & 25 & 38 & 62 & 49 & 63 & 29 & 74 & 82 \\ \hline \text { Posttest } & 29 & 45 & 51 & 45 & 71 & 32 & 74 & 87 \end{array} $$
Problem 4
Lengths of Prison Sentences A random sample of men and women in prison was asked to give the length of sentence each received for a certain type of crime. At \(\alpha=0.05,\) test the claim that there is no difference in the sentence received by each gender. The data (in months) are shown here. $$\begin{aligned}&\begin{array}{l|ccccccccc}\text { Males } & 8 & 12 & 6 & 14 & 22 & 27 & 32 & 24 & 26 \\\\\hline \text { Females } & 7 & 5 & 2 & 3 & 21 & 26 & 30 & 9 & 4\end{array}\\\&\begin{array}{l|ccccc}\text { Males } & 19 & 15 & 13 & & \\\\\hline \text { Females } & 17 & 23 & 12 & 11 & 16\end{array}\end{aligned}$$
Problem 5
A university dean wishes to see if there is a difference in the number of credits community college students transfer as opposed to students who attend a 4-year college and transfer after 2 years. The data are shown. Use the Wilcoxon rank sum test to test this claim at \(\alpha=0.05 .\) $$\begin{array}{l|llllllllll}\text { Community } & & & & & & & & & & \\\\\text { College } & 61 & 63 & 42 & 35 & 48 & 62 & 64 & 60 & 59 & 65 \\\\\hline \text { Four-Year } & & & & & & & & & & \\\\\text { Schools } & 58 & 64 & 37 & 46 & 45 & 63 & 71 & 58 & 68 & 66\end{array}$$
Problem 5
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 median age at first marriage in 2014 for women was 27 years - the highest it has ever been. A random sample of women's ages (in years) from recently applied for marriage licenses resulted in the following set of ages. At \(\alpha=0.05,\) is there sufficient evidence that the median is not 27 years? $$ \begin{array}{lllll} 34.6 & 31.2 & 28.9 & 28.4 & 24.3 \\ 29.8 & 25.9 & 21.4 & 25.1 & 26.2 \\ 28.3 & 30.6 & 35.6 & 34.2 & 34.1 \end{array} $$
Problem 5
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? $$ \begin{array}{l|rrrrrrr} \text { Grade } \mathbf{4} & 90 & 84 & 80 & 87 & 88 & 77 & 79 \\ \hline \text { Grade } \mathbf{8} & 81 & 75 & 66 & 76 & 80 & 59 & 74 \end{array} $$
