6. The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance. The study focuses on "round-trip" traders, i.e., trades in which the same stock was both bought and sold in the same quarter. Consider a random sample of 200 round-trip traders made by institutional investors. Suppose the sample mean rate of return is 2.50% and the sample deviation is 8.85%. If the true mean rate of return of round-trip trades is positive, then the population of institutional investors is considered to have performed successfully. a. Specify the null and alternative hypotheses for determining whether the population institutional investors performed successfully. b. Calculate the test statistic. c. Use either rejection region or p-value approach to give the appropriate conclusion at a = .01.

1. A researcher suspects that the actual prevalence of depression among children and adolescents is higher than was previously reported. The previously reported prevalence for depression among children and adolescents was 12.5%, and the researcher conducts a study to test the accuracy of the previously reported prevalence of depression among children and adolescents by recruiting 100 total children or adolescents and tests them for depression using the DSM-5. The researcher determines that the prevalence of depression from the study is 12.9% and the standard deviation was 0.4. What should the researcher’s conclusion be for a 5% significance level? Choose from the following.    A) We reject H0 at the 5% level because 10 is greater than 1.96. We do have statistically significant evidence to show the actual prevalence of depression among children and adolescents is above the previously reported prevalence of 12.5%.   B) We fail to reject H0 at the 5% because -10 is less than 1.645. We do…

1.Suppose a used car dealer runs autos through a two-stage process to get them ready to sell. The mechanical checkup costs $50 per hour and takes an average of 90 minutes, with a standard deviation of 15 minutes. The appearance prep (wash, polish, etc.) costs $6 per hour and takes an average of 60 minutes, with a standard deviation of 5 minutes. What are the mean and standard deviation of the total time spent preparing a car? (Note that we cannot find the standard deviation if we do not believe that the two phases of the process are independent, an important assumption to check.) b). What are the mean and standard deviation of the total expense to prepare a car? c). What are the mean and standard deviation of the difference in costs for the two phases of the operation? d). What is the probability that it will take longer to do the appearance prep than the mechanical checkup? (Note that we cannot answer this question unless we believe each phase of the process can be described by a…

An investment company is promoting their mutual investment funds. Their fund specializing in the Hong Kong stock market has been consistently outperforming the Hang Seng Index over the last ten years. The company argues that such strong performance is proof of their great ability in selecting stocks for long-term investment.     Based on your understanding of the data generating process and the possible biases associated with it, provide an alternative interpretation of the statistics about fund performance.