1. Elevated levels of plasma HDL cholesterol may be associatedwith lowered risk of coronary heart disease. Several studies havesuggested that vigorous exercise may result in increased levels ofHDL cholesterol. To investigate this theory, researchers measuredHDL concentrations (mg/dL) in middle-aged (35-66 years) marathonrunners, as well as inactive men. The data are summarized below.(Assume equal population variances in the two groups.)

sample size mean st. dev

Inactive men 70 43.3 14.2

Marathon runners 70 52.8 14.3

a. (4pts) Conduct a hypothesis test to see if marathon runnershave significantly lower mean HDL cholesterol levels in this agegroup. Use α=0.05. Write your hypotheses, calculate the teststatistic, and p-value, and write your conclusion. (SE = 2.41)

b. (2pts) Calculate the 90% confidence interval for thedifference in mean HDL cholesterol among inactive men and marathonrunners in this age group. Interpret your interval.

c. (1pt) State two ways in which the confidence interval in (i)could be made narrower.

d. (1pt) Use your interval in (b), Explain how this confidenceinterval corresponds to the results you found in part (a).

2. As part of a study of environmental influences on sexdetermination in the fish Menidia, eggs from a single mating weredivided into two groups and raised in either a warm or a coldenvironment. The data show that 65 of 141 offspring in the warmenvironment and 107 of 169 offspring in the cold environment werefemales.

a. Test the hypothesis that the distribution of female and malefish follows a 1:1 ratio in the cold environment. Ascertain thatyour assumptions are met, and then do the test. (2pts)

b. What are the odds of the fish in the cold environment beingfemale? (1pt)

c. Calculate the odds ratio of the fish being female in the coldenvironment compared to the warm environment. Interpret this oddsratio in the context of the question. (1pt)