Psychology: Rat Colonies A psychology professor is

Statistical Literacy For data pairs (x, y), if y always increases as x increases, is the relationship monotone increasing, monotone decreasing, or nonmonotone?

Statistical Literacy Consider the Spearman rank correlation coefficient rs for data pairs (x, y). What is the monotone relationship, if any, between x and y implied by a value of (a) rs 0? (b) rs close to 1? (c) rs close to 1?

For Problems 3–11, please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Compute the sample test statistic. (c) Find or estimate the P-value of the sample test statistic. (d) Conclude the test. (e) Interpret the conclusion in the context of the application. Training Program: Sales A data processing company has a training program for new salespeople. After completing the training program, each trainee is ranked by his or her instructor. After a year of sales, the same class of trainees is again ranked by a company supervisor according to net value of the contracts they have acquired for the company. The results for a random sample of 11 salespeople trained in the last year follow, where x is rank in training class and y is rank in sales after 1 year. Lower ranks mean higher standing in class and higher net sales. Using a 0.05 level of significance, test the claim that the relation between x and y is monotone (either increasing or decreasing).

Economics: Stocks As an economics class project, Debbie studied a random sample of 14 stocks. For each of these stocks, she found the cost per share (in dollars) and ranked each of the stocks according to cost. After 3 months, she found the earnings per share for each stock (in dollars). Again, Debbie ranked each of the stocks according to earnings. The way Debbie ranked, higher ranks mean higher cost and higher earnings. The results follow, where x is the rank in cost and y is the rank in earnings. Stock 1 2 3 4 5 6 7 8 9 10 11 12 13 14 x rank 5 2 4 7 11 8 12 3 13 14 10 1 9 6 y rank 5 13 1 10 7 3 14 6 4 12 8 2 11 9 Using a 0.01 level of significance, test the claim that there is a monotone relation, either way, between the ranks of cost and earnings.

Psychology: Rat Colonies A psychology professor is studying the relation between overcrowding and violent behavior in a rat colony. Eight colonies with different degrees of overcrowding are being used. By using a television monitor, lab assistants record incidents of violence. Each colony has been ranked for crowding and violence. A rank of 1 means most crowded or most violent. The results for the eight colonies are given in the following table, with x being the population density rank and y the violence rank. Colony 1 2 3 4 5 6 7 8 x rank 3 5 618 7 4 2 y rank 1 3 528 6 4 7 Using a 0.05 level of significance, test the claim that lower crowding ranks mean lower violence ranks (i.e., the variables have a monotone-increasing relationship).

FBI Report: Murder and Arson Is there a relation between murder and arson? A random sample of 15 Midwest cities (over 10,000 population) gave the following information about annual number of murder and arson cases. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) 688 Chapter 12 NONPARAMETRIC STATISTICS (i) Rank-order murder using 1 as the largest data value. Also rank-order arson using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. (ii) Use a 1% level of significance to test the claim that there is a monotoneincreasing relationship between the ranks of murder and arson

Psychology: Testing An army psychologist gave a random sample of seven soldiers a test to measure sense of humor and another test to measure aggressiveness. Higher scores mean greater sense of humor or more aggressiveness. Soldier 1 2 3 4 5 6 7 Score on humor test 60 85 78 90 93 45 51 Score on aggressiveness test 78 42 68 53 62 50 76 (i) Ranking the data with rank 1 for highest score on a test, make a table of ranks to be used in a Spearman rank correlation test. (ii) Using a 0.05 level of significance, test the claim that rank in humor has a monotone-decreasing relation to rank in aggressiveness

FBI Report: Child Abuse and Runaway Children Is there a relation between incidents of child abuse and number of runaway children? A random sample of cities (over 10,000 population) gave the following information about the number of reported incidents of child abuse and the number of runaway children. (Reference: Federal Bureau of Investigation, U.S. Department of Justice.) (i) Rank-order abuse using 1 as the largest data value. Also rank-order runaways using 1 as the largest data value. Then construct a table of ranks to be used for a Spearman rank correlation test. (ii) Use a 1% level of significance to test the claim that there is a monotoneincreasing relationship between the ranks of incidents of abuse and number of runaway children

Demographics: Police and Fire Protection Is there a relation between police protection and fire protection? A random sample of large population areas gave the following information about the number of local police and the number of local fire-fighters (units in thousands). (Reference: Statistical Abstract of the United States.)

Ecology: Wetlands Turbid water is muddy or cloudy water. Sunlight is necessary for most life forms; thus turbid water is considered a threat to wetland ecosystems. Passive filtration systems are commonly used to reduce turbidity in wetlands. Suspended solids are measured in mg/l. Is there a relation between input and output turbidity for a passive filtration system and, if so, is it statistically significant? At a wetlands environment in Illinois, the inlet and outlet turbidity of a passive filtration system have been measured. A random sample of measurem

Insurance: Sales Big Rock Insurance Company did a study of per capita income and volume of insurance sales in eight Midwest cities. The volume of sales in each city was ranked, with 1 being the largest volume. The per capita income was rounded to the nearest thousand dollars. City 1 2 3 4 5 6 7 8 Rank of insurance sales volume 671 8 3 25 4 Per capita income in $1000 17 18 19 11 16 20 15 19 (i) Using a rank of 1 for the highest per capita income, make a table of ranks to be used for a Spearman rank correlation test. (ii) Using a 0.01 level of significance, test the claim that there is a monotone relation (either way) between rank of sales volume and rank of per capita income