Exam 11: Nonparametric Tests Online and CD Only

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -The number of absences and the final grades of 9 randomly selected students from a statistics class are given below. Can you conclude that there is a correlation between final grade and number of absences? Use $\alpha$ = 0.01. Number of Absences 0 3 6 4 9 2 15 8 5 Final Grade 98 86 80 82 71 92 55 76 82

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A government agency claims that the median hourly wages for workers at fast food restaurants in the western U.S. is $6.35. In a random sample of 100 workers, 68 were paid less than $6.35, 10 were paid $6.35, and the rest more than $6.35. Test the governmentʹs claim. Use $\alpha = 0.05 .$

Perform the indicated Kruskall-Wallis test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A researcher wishes to compare times it takes workers to assemble a certain computer component using different machines. Workers are randomly selected and randomly assigned to one of three different machines. The time (in minutes)it takes each worker to assemble the component is recorded. Use the Kruskal-Wallis test to test the claim that there is a difference in the distributions of the assembly times for the three machines. Use $\alpha = 0.05$ Machine 1 Machine 2 Machine 3 43 51 39 42 40 36 43 49 40 41 44 42 44 46 41 42 43 38 43 47 48

A college researcher claims that the median hours worked by full time students is at least 10 hours per week. In a random sample of 100 students, 65 worked more than 10 hours, 10 worked exactly 10 hours and the rest Worked less than 10 hours. Find the critical value to test the researcherʹs claim. Use $\alpha$ = 0.05.

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The results are listed below. The subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested again. The results are listed below. (All units are milligrams per deciliter.)Use the sign test to test the companyʹs claim that the drug lowers cholesterol levels. Use $\alpha$ = 0.01. Subject 1 2 3 4 5 6 7 8 9 10 Before 220 231 230 215 241 254 179 199 171 186 After 205 226 238 205 236 254 149 181 169 171

A convenience store owner believes that the median number of lottery tickets sold per day is 49. A random sample of 20 days yields the data below. Find the critical value to test the ownerʹs claim. $\alpha = 0.05 .$ 32 48 59 64 31 55 70 27 33 38 47 54 54 44 44 49 49 59 54 38

An airport security officer manually searched carry-on bags of people boarding a plane in the sequence shown, where S represents a searched bag and N represents a bag not searched. Find the test statistic z to test for randomness.

A weight-lifting coach claims that a weight-lifter can increase strength by taking vitamin E. To test the theory, the coach randomly selects 9 athletes and gives them a strength test using a bench press. The results are listed Below. Thirty days later, after regular training supplemented by vitamin E, they are tested again. The new Results are listed below. Find the critical value for a Wilcoxon signed-rank test to test the claim that the vitamin E supplement is effective in increasing the athletesʹ strength. Use $\alpha$ = 0.05. Athlete 1 2 3 4 5 6 7 8 9 Befor 230 233 247 202 201 193 232 239 198 After 240 238 247 200 208 208 237 234 203

A pharmaceutical company wishes to test a new drug with the expectation of lowering cholesterol levels. Ten subjects are randomly selected and their cholesterol levels are recorded. The results are listed below. The Subjects were placed on the drug for a period of 6 months, after which their cholesterol levels were tested Again. The results are listed below. (All units are milligrams per deciliter.)Use the Wilcoxon signed-rank test to Find the test statistic $\mathrm { W } _ { \mathrm { S } }$ to test the companyʹs claim that the drug lowers cholesterol levels. Subject 1 2 3 4 5 6 7 8 9 10 Before 219 245 253 200 244 243 238 197 227 224 After 204 240 261 190 239 243 208 179 225 209

Perform the indicated Kruskall-Wallis test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -Four different types of fertilizers are used on raspberry plants. The number of raspberries on each randomly selected plant is given below. Use the Kruskal-Wallis test to test the claim that there is no difference in the distributions of the number of raspberries for the four different types of fertilizer. Use $\alpha$ α = 0.05. 8 Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 4 9 8 9 6 8 11 6 8 9 8 7 6 10 8 6 7 10 8 5 8 9 9 6 7 6 6 7

A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The Data, in years, are listed below. What is the appropriate test to test the claim that there is no difference in the Sentence received by each sex? Men 12 24 18 20 21 28 Women 11 14 11 16 28 14 Men 16 24 14 21 25 26 Women 36 10 12 15 19 29

A researcher wants to know if the time spent in prison for a particular type of crime was the same for men and women. A random sample of men and women were each asked to give the length of sentence received. The Data, in years, are listed below. Use the Wilcoxon rank sum test to find R, the sum of the ranks for the smaller Sample, to test the claim that there is no difference in the sentence received by each gender. Men 11 23 17 19 20 27 Women 10 13 10 15 27 13 Men 15 23 13 20 24 25 Women 35 9 11 14 18 28

Use the sequence to find the values of $\mathrm { n } _ { 1 } \text { and } \mathrm { n } _ { 2 }$ $\text { L L L R LR L R R L L LR R }$

Use the Spearman rank correlation coefficient to determine whether the correlation between the given variables is significant. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A manager wishes to determine whether there is a relationship between the distance traveled per month by the sales representatives and the amount of sales generated per month. Can you conclude that there is a correlation between distance traveled and sales generated? Use $\alpha$ = 0.05. Distance (hundreds of miles) 11 12 19 16 17 24 12 10 20 Sales (thousands of dollars) 40 42 87 71 74 70 57 64 129

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -A college researcher claims that the median time worked by full time students is at least 10 hours per week. In a random sample of 100 students, 59 worked more than 10 hours, 10 worked exactly 10 hours and the rest worked less than 10 hours. Test the researcherʹs claim. Use $\alpha = 0.05$

A physician claims that a personʹs diastolic blood pressure can be lowered, if, instead of taking a drug, the person listens to a relaxation tape each evening. Ten subjects are randomly selected. Their blood pressures, Measured in millimeters of mercury, are listed below. The 10 patients are given the tapes and told to listen to Them each evening for one month. At the end of the month, their blood pressures are taken again. The data are Listed below. Find the critical value for a Wilcoxon signed-rank test to test the physicianʹs claim. Use $\alpha$ = 0.05. Patient 1 2 3 4 5 6 7 8 9 10 Before 84 98 87 92 82 80 97 85 91 90 After 81 92 87 84 76 69 100 75 87 74

A college researcher claims that the median hours worked by full time students is at least 13 hours per week. In a random sample of 100 students, 58 worked more than 13 hours, 10 worked exactly 13 hours and the rest Worked less than 13 hours. Find the test statistic to test the researcherʹs claim.

Perform the indicated Kruskall-Wallis test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -The grade point averages of students participating in different sports at a college are to be compared. The data are listed below. Use the Kruskal-Wallis test to test the claim that there is a difference in the distribution of the GPAs of the three different sports groups. Use $\alpha = 0.05 .$ Tennis Golf Swimming 3.6 2.2 3.1 3 2.5 3.4 2.9 3.7 3.2 3.9 2.3 2.9 3.5 2.7 2.9 2.5 2.4 2.8

A medical researcher wishes to try three different techniques to lower blood pressure of patients with high blood pressure. The subjects are randomly selected and assigned to one of three groups. Group 1 is given Medication, Group 2 is given an exercise program, and Group 3 is assigned a diet program. At the end of six Weeks, the reduction in each subjectʹs blood pressure is recorded. Use the Kruskal-Wallis test to find the critical Value to test the claim that there is no difference in the distribution of the populations. Use $\alpha$ = 0.05. Group 1 Group 2 Group 3 13 10 8 14 7 14 11 4 6 17 5 10 15 6 11 10 2 6

Perform the indicated sign test. Be sure to do the following: Identify the claim mathematically and state the null and alternative hypotheses. Determine the critical value and find the test statistic. Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim. -Test the hypothesis that the median age of statistics teachers is less than 45 years. A random sample of 60 statistics teachers found 25 above 45 years, 33 below 45 years, and the rest exactly 45 years. Use $\alpha = 0.01 .$