Tough......... Solve carefully

CHALLENGE PROBLEMS 43. Ralph Rollins, a researcher, believes that the stocks of firms that have appeared in a certain financial newspaper with a positive headline and story return more on a risk-adjusted basis. He gathers data on the risk-adjusted returns for these stocks over the six months after they appear on the cover, and data on the misk-adjusted returns for an equal-sized sample of firms with characteristics similar to the cover-story firms matched by time period. A. State the likely null and alternative hypotheses for a test of his belief. B. Is this a one- or two-tailed test? C Describe the steps in testing a hypothesis such as the null you stated in part A. 44. For each of the following hypotheses, describe the appropriate test, identify the appropriate test statistic, and explain under what conditions the null hypothesis should be rejected. A. A researcher has returns over 52 weeks for an index of natural gas stocks and for an index of oil stocks and wants to know if the weekly returns are equal. Assume that the returns are approximately normally distributed B. A researcher has two independent samples that are approximately normally distributed. She wishes to test whether the mean values of the two random variables are equal and assumes that the variances of the populations from which the two samples are drawn are equal. As an additional question here, how should the degrees of freedom be calculated? C. A researcher wants to determine whether the population variances of two normally distributed random variables are equal based on two samples of sizes nl and n2. As an additional question here, how should the degrees of freedom be calculated? D. A researcher wants to test whether the variance of a normally distributed population is equal to 0.00165. As an additional question here, how should the degrees of freedom be calculated