FIN 330

Homework 4

1. For this problem use data contained in the Excel file Paired. The data were actually collected in pairs, and each row represents a pair.

1. Suppose that we ignore the fact that the data were collected in pairs and mistakenly treat this as a two-sample problem. Perform a t-test (for two samples assuming unequal variances). [ DataAnalysis t-test: two sample assuming unequal variances] . Include print out of the tests output.
2. From the test output find the two-sample t-statistic, degrees of freedom, and P-value for the two-sided alternative.
3. State null hypothesis that is being tested. Would you reject the null hypothesis at 5% significance level? At 10% significance level?
4. Now analyze the data in the proper way. Construct sample of the differences. Perform a one sample t-test [ You will need to create a dummy sample; make all observations in the dummy sample equal to zero; size of the dummy sample may be different from the size of your sample of diffrences. Next use t-test: two sample assuming unequal variances]. Include print out of the tests output.
5. From the test output find the two-sample t-statistic, degrees of freedom, and P-value for the two-sided alternative.
6. State null hypothesis that is being tested. Would you reject the null hypothesis at 5% significance level? At 10% significance level?
7. Describe the differences in the two test results.

2. Refer to the previous exercise. Perhaps an easier way to see the major difference in the two analysis approaches for these data is by computing 95% confidence intervals for the mean difference.

1. Compute the 95% confidence interval using the two-sample t confidence interval.
2. Compute the 95% confidence interval using the matched pairs t confidence interval.
3. Compare the estimates (that is, the centers of the intervals) and margins of error. What is the major difference between the two approaches for these data?

3. A stockbroker determines the short-run direction of the market using the average quarterly return of stock mutual funds. He believes the next quarter will be profitable when the average is greater than 1%. He will get complete quarterly return information soon, but right now he has data from a random sample of 30 stock funds. The mean quarterly return in the sample is 1.5%, and the standard deviation is 1.9%. Based on this sample, test to see if the broker will feel the next quarter will be profitable.

1. State appropriate null and alternative hypotheses. Explain how you decided between the one- and two-sided alternatives.
2. Find the t statistic, degrees of freedom, and P-value. State your conclusion using the =0.05 significance level.

Group1 Group2 48.88 52.63 52.55 50.94 48.9 50.6 51.0 48.0 54.2 53.02 50.7 45.9 48.8 48.44 47.848.92 51.1 50.66 47.78 51.63