Reference no: EM132856927

1. The standard deviation of a normally distributed population is equal to 10. A sample size of 25 is selected, and its mean is found to be 95.

a.) Find an 80% confidence interval for μ.

b.) If the sample size were 100 what would be the 80% confidence interval?

c.) If the sample size was 25 but the standard deviation was 5, what would be the 80% confidence interval?

2. We are interested in estimating the mean life of a new product. How large a sample do we need to take in order to estimate the mean to within 1/10 of a standard deviation with 90% confidence?

3. The public relations officer for a particular city claims the average monthly cost for childcare outside the home for a single child is $700. A potential resident is interested in whether the claim is correct. She obtains a random sample of 64 records and computes the average monthly cost of childcare to be $689. Assume the population standard deviation to be $40.

a.) Perform the appropriate test of hypothesis for the potential resident using α = 0.01.

Step 1

Step 2

Step 3

Step 4

b.) Find the p-value for the test in a.).

c.). What effect, if any, would there be on the conclusion in part if you change α to 0.05?

d.) Find the power of the test when μ is actually $685 and α = 0.05.