Short Answer Questions

Section A: Short Answer Questions and Fill in the Blank Questions (60 points). 1. A study by a bank compared the average savings of customers who were depositors for three years or less, with those who had been depositors for more than three years. The results of a sample are: Assuming that the financial officer wants to show that there is a difference in the average savings balance between the two classes of depositors, what is the null hypothesis? _____________________ 2. If we are testing for the difference between two population means and assume that the two populations have equal but unknown standard deviations, then the test has _________ degrees of freedom. 3. The pooled estimate of the proportion is found by dividing the total number of successes by __________________________. 4. If we are testing for the difference between two population means and assume that the two populations have equal and unknown standard deviations, the standard deviations are _____. 5. When independent samples with unknown but equal standard deviations are used to test for differences in the means, we pool the sample ________________. 6. The paired t test is especially appropriate when the sample sizes of two groups are _______.  7. The paired difference test has ___________ degrees of freedom. 8. When testing the difference between two population means, the hypothesized difference is _______________. 9. When testing the difference between two population proportions, the hypothesized difference is _______________. 10. A statistics professor wants to compare grades in two different classes of the same course. This is an example of _________ populations. Section B: Hypothesis Testing (40 points). 11. A financial planner wants to compare the yield of income and growth mutual funds. Fifty thousand dollars is invested in each of a sample of 35 income and 40 growth funds. The mean increase for a two-year period for the income funds is $900. For the growth funds the mean increase is $875. Income funds have a sample standard deviation of $35; growth funds have a sample standard deviation of $45. Assume that the population standard deviations are equal. At the 0.05 significance level, is there a difference in the mean yields of the two funds? What decision is made about the null hypothesis using and a = 0.05? ____________ 12. A company is researching the effectiveness of a new web site design to decrease the time to access a website. Five web site users were randomly selected and their times (in seconds) to access the web site with the old and new designs were recorded. The results follow.

Let  = 0.05. Is the mean time to access the new web site design shorted? Express your answer in terms of the null hypothesis. 

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