Exam 15: Nonparametric Statistics

Choose the one alternative that best completes the statement or answers the question. -The owner of a major golf course believes that the course is so tough that most golfers rarely break par of $75 .$ The scores from a random sample of 20 golfers are listed below. Find the critical value to test the club owner's hypothesis. Use $\alpha = 0.05$ . 74 72 75 75 78 77 69 81 75 80 72 74 76 76 83 81 75 77 78 68

Choose the one alternative that best completes the statement or answers the question. -A real estate agent surmises that the median rent for a studio apartment in a mountain community in Colorado is less than $\$ 2000$ per month. The rents for a random sample of 15 studio apartments are listed below. Find the critical value to test the agent's hypothesis. Use $\alpha = 0.01$ . \ 2300 \ 2250 \ 1700 \ 1875 \ 1735 \ 2750 \ 2175 \ 1670 \ 2390 \ 3000 \ 1995 \ 2000 \ 2075 \ 2000 \ 1780

Write the word or phrase that best completes each statement or answers the question. -Test the hypothesis that the median age of music teachers is 44 years. A random sample of 60 music teachers found 25 above 44 years and 35 below 44 years. Use $\alpha = 0.01$ .

Write the word or phrase that best completes each statement or answers the question. -The ages and average monthly prescription drug bills (in dollars) of 9 randomly selected adults are given below. Can you conclude that there is a correlation between age and amount spent on prescription drugs? Use $\alpha = 0.05$ . Age 38 41 45 48 51 53 57 61 65 Drug Bill 116 120 123 131 142 145 148 150 152

Provide an appropriate response. -A researcher wants to know if the time spent in prison for grand larceny was the same for men and women. A random sample of men and women convicted of grand larceny were each asked to give the length of sentence received. The data, in years, are listed below. Test the hypothesis that the median sentence for men is greater than the median sentence for women. Use $\alpha = 0.10$ . Men 22 34 28 30 31 38 Women 21 24 21 26 38 24 Men 26 34 24 31 35 36 Women 46 20 22 25 29 39

Provide an appropriate response. -Mathematics SAT scores for students randomly selected from two different schools are listed below. Test the hypothesis that the median scores in the schools are different. Use $\alpha = 0.05$ .

Provide an appropriate response. -Use the Wilcoxon matched-pairs signed-ranks test to test the given hypothesis at the $\alpha = 0.05$ level of significance. The dependent samples were obtained randomly. Hypotheses: $\mathrm { H } _ { 0 } : \mathrm { M } _ { \mathrm { D } } = 0$ versus $\mathrm { H } _ { 1 } : \mathrm { M } _ { \mathrm { D } } \neq 0$ with $\mathrm { n } = 45 , \mathrm {~T} _ { + } = 152$ , and $\mathrm { T } _ { - } = 883$

Write the word or phrase that best completes each statement or answers the question. -A manager wishes to determine the relationship between the average number of new accounts opened by 9 sales representatives (per month) and their sales (in thousands of dollars) per month. Can you conclude that there is a correlation between the new accounts opened and sales generated? Use $\alpha = 0.05$ . Number of New Accounts 9 10 17 14 15 22 10 8 18 Sales 38 40 85 69 72 68 55 62 127

Write the word or phrase that best completes each statement or answers the question. -The history department at a college asked its professors and students to rank 8 guest speakers according to their communication skills. The data are listed below. A 10 is the highest ranking and a 1 the lowest ranking. Test the hypothesis of no correlation between the rankings. Use $\alpha = 0.05$ . Speaker 1 2 3 4 5 6 7 8 Professors 2 3 6 10 8 1 5 4 Students 4 3 1 4 5 7 9 6

Write the word or phrase that best completes each statement or answers the question. -A government agency believes that the median hourly wages for retail store workers in the central U.S. is $\$$ 6.85. In a random sample of 100 workers, 68 were paid less than $\$ 6.85$ , 10 were paid $\$ 6.85$ , and the rest more than $\$ 6.85$ . Test the government's hypothesis. Use $\alpha = 0.05$ .

Choose the one alternative that best completes the statement or answers the question. -The owner of a major golf course believes that the course is so tough that most golfers rarely break par of $69 .$ The scores from a random sample of 20 golfers are listed below. Find the test statistic $x$ to test the club owner's hypothesis. Use $\alpha = 0.05$ . 68 66 69 69 72 71 63 75 69 74 66 68 70 70 77 75 69 71 72 62

Provide an appropriate response. -The two flavors of ice cream in a taste test are supposed to be administered to respondents in a random fashion. Suspecting that the administrators of the test did not follow the randomness rule, the project statistician examines the flavor order for the day's taste testing, shown below. chocolate neopolitan chocolate neopolitan neopolitan neopolitan chocolate neopolitan chocolate chocolate neopolitan chocolate neopolitan chocolate neopolitan chocolate neopolitan chocolate neopolitan chocolate Is there evidence at the $\alpha = 0.05$ level of significance to support the hypothesis that the flavor order is not random?

Choose the one alternative that best completes the statement or answers the question. -In order to be able to use the Mann-Whitney Test, the samples must be the same size and independent.

Choose the one alternative that best completes the statement or answers the question. -A real estate agent surmises that the median rent for a studio apartment in a mountain community in Colorado is less than $\$ 1100$ per month. The rents for a random sample of 15 studio apartments are listed below. Find the test statistic x to test the agent's hypothesis. Use $\alpha = 0.01$ . \ 1400 \ 1350 \ 800 \ 975 \ 835 \ 1850 \ 1275 \ 770 \ 1490 \ 2100 \ 1095 \ 1100 \ 1175 \ 1100 \ 880

Choose the one alternative that best completes the statement or answers the question. -A government agency believes that the median hourly wages for retail store workers in the central U.S. is $\$ 6.90$ . In a random sample of 100 workers, 68 were paid less than $\$ 6.90,10$ were paid $\$ 6.90$ , and the rest more than $\$$ 6.90. Find the test statistic $z$ to test the government's hypothesis. Use $\alpha = 0.05$ .

Choose the one alternative that best completes the statement or answers the question. -A pharmaceutical company wishes to test a new drug with the expectation of weight reduction. Ten subjects are randomly selected and their weights are recorded. The subjects were placed on the drug for a period of 6 months, after which their weights were recorded again. The results are listed below. (All units are pounds.) Use the Wilcoxon signed-ranks test to find the test statistic T to test the company's hypothesis that the drug reduces weight. Use $\alpha = 0.05$ . Subject 1 2 3 4 5 6 7 8 9 10 Before 253 254 255 201 258 170 241 266 270 248 After 238 249 263 191 253 170 211 248 268 233

Provide an appropriate response. -___________________ statistical processes are often called distribution free procedures.

Provide an appropriate response. -The table below lists the amounts (in dollars) spent on clothing and entertainment over the last year by 10 adults selected at random. Find the test statistic $\mathrm { r } _ { \mathrm { S } }$ , to test the hypothesis of no correlation between spending in these two areas. Use $\alpha = 0.05$ . Clothing 395 480 485 390 470 Entertainment 480 550 575 510 560 Clothing 500 400 450 520 410 Entertainment 525 610 530 400 410

Provide an appropriate response. -A convenience store owner believes that the median number of newspapers sold per day is 73 . A random sample of 20 days yields the data below. Find the critical value to test the owner's hypothesis. Use $\alpha = 0.05$ . 56 72 83 88 55 79 94 51 57 62 71 78 78 68 68 73 73 83 78 62

Choose the one alternative that best completes the statement or answers the question. -A college dean believes that the median hours spent studying by full time students is at least 10 hours per week. In a random sample of 100 students, 61 studied more than 10 hours, 10 studied exactly 10 hours and the rest studied less than 10 hours. Find the test statistic to test the dean's hypothesis. Use $\alpha = 0.05$ .