Question

Does stock in IBM return a different amount on average than T-Bills? We will attempt to answer this question by using a dataset of the 264 monthly returns from IBM between 1990 and 2011. Over this period, the mean of the monthly IBM returns was 1.26% and the standard deviation was 8.27%. We will take as given that the expected monthly returns from investing in T-Bills is 0.3%.

1. What is the sample? What are the sample mean and standard deviation?
2. What is the relevant population? What are the interpretations of population mean and standard deviation?
3. What are the null and alternative hypotheses for testing whether or not IBM gives a different expected return from T-Bills (0.3%)?
4. Use an appropriate test statistic to summarize the evidence against the null hypothesis (which is asking to state the test statistic and compute the observed test statistic)
5. What is the rejection region for your test statistic in ((4)) at significance level 5%?
6. If the null hypothesis were true (there were no difference in expected monthly returns between IBM and T-Bills) what would be the chance of observing data at least as extreme as observed?
7. Is there compelling evidence (at significance level 5%) of a difference in expected monthly returns between IBM and T-Bills? Use your answers from (5)
8. Is there compelling evidence (at significance level 5%) of a difference in expected monthly returns between IBM and T-Bills? Use your answers from (6).
9. Construct a confidence interval for the population mean with confidence level 99%.
10. Based on the result in ((9)), can you conclude that there is compelling evidence at significance level 1% of a difference in expected monthly returns between IBM and T-Bills? Why?