A clinical psychologist is interested in the relationship between testosterone level in married males and the quality of their marital relationship. A study is conducted in which the testosterone levels of eight married men are measured. The eight men also fill out a standardized questionnaire assessing quality of marital relationship. The questionnaire scale is 0–25, with higher numbers indicating better relationships. Testosterone scores are in nanomoles/liter of serum. The data are shown below. Subject Number 1 2 3 4 5 6 7 8 Relationship Score 24 15 15 10 19 11 20 19 Testosterone Level 12 13 19 25 M 16 15 21 a.       Determine the least-squares regression line for predicting relationship score from testosterone level. b.      What percentage of the variance in relationship score is accounted for by the regression equation? c.        Can we conclude that there is a significant relationship between the testosterone level and the relationship score? Use the 5% significance level. M – your birth month.

(Use SPSS) A random sample of nine male race horses at a Fauquier County stable yielded the following data on age of horse (months) and time to run a mile (seconds). Age of Horse (x) 22 27 62 47 38 ☐32 55 50 58 Time to Run a Mile (y) 96 102 158 125 113 107 142 139 141 a. Construct a scatterplot of the data. What does it suggest about the relationship between the age and speed of male race horses in Fauquier County? b. Assuming that the simple linear regression model is appropriate, obtain the equation of the estimated regression line. c. What percentage of the observed variation in Time to Run a Mile can be explained by the resulting model? d. Check the regression assumptions using a normal probability plot of the residuals and a plot of the explanatory variable values versus the studentized residuals. e. A race horse trainer in Fauquier County claimed that there is a useful linear relationship between the two variables. Do you agree? Carry out a formal hypothesis test to support your…

A college administrator wants to know if there is a significant difference between sexual orientation and level of family support for students at their college. The administrator takes a random sample of students who identify as gay/lesbian, bisexual or heterosexual/straight. There were 22 students sampled in each category. A measure of family support is given with higher scores indicating more family support. The means are as follows: Gay/lesbian Bisexual Heterosexual/Straight MG/L = 16 MBi = 17 MH/S = 22   Source SS df MS F Orientation 300       Error 2961       Total           What is the value of MS error?

A county environmental agency suspects that the fish in a particular polluted lake have elevated mercury levels. To confirm that suspicion, five striped basses in that lake were caught and their tissues were tested for mercury. For the purpose of comparison, four striped basses in an unpolluted lake were also caught and tested. The fish tissue mercury levels in mg/kg are given below. Sample I(From Polluted Lake) 0.523 0.723 0.523 0.623 0.523 Sample II(From Unpolluted Lake) 0.323 0.223 0.523 0.323 0.000 (a) Construct the 95% confidence interval for the difference in the population means based on these data. (b) Test, at the 5% level of significance, whether the data provide sufficient evidence to conclude that fish in the polluted lake have elevated levels of mercury in their tissue.