1. You run a bank and want to estimate the bank's average number of customers per day (the population is all the days you are open for business in a year).You take a random sample of 10 days and record the numbers of customers on those days.The sample data is shown below.

450 470 430 420 490

440 460 420 500 420

1. The estimated variance of the sample mean is.
2. What is a 95% confidence interval for the bank's average number of customers per day?
3. As the manager of the bank in the previous question, you want the 95% interval estimate to capture the population mean customers per day within 10 customers.Using a planning value of = 35, how many days should you include in the sample?
4. You work for a charitable organization and you want to estimate the average age of the people who donate to your organization.You get a random sample of n = 120 donors and the value of the sample mean is 42 years.The value of the sample standard deviation is 19 years. The lower and upper end of the 95% confidence interval for the average age of people who donate to your organization are:
5. In the previous question you want to test the hypothesis, at the 5 percent level of significance, that the average age is at least 45 years.Compute the probability value for the test.
6. Regardless how you answered the previous question, which of the following statements is correct?
7. If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type II error.
8. If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type I error.
9. If the mean age is less than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type I error.
10. If the mean age is in at least than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type II error.
11. According to the Census Bureau the sample proportion of American children without health insurance rose from 0.109 in 2005 to 0.117 in 2006.Using the Census data you test the hypothesis that the change in the population proportion of American children without health insurance is zero with a Probability of Type I error = 0.05.You reject the zero change hypothesis.
12. To test the hypothesis, at a 5% level of significance, that the proportion of American children without health insurance has increased from 0.109, a random sample of 1020 children revealed a sample proportion of 0.121.Compute the p-value.