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A) i) a. In a random sample of 200 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes.

b. Repeat part (a) withn= 500.

c. Repeat part (a) withn= 1000.

d. Describe the effect on the confidence interval estimate of increasing the sample size.

A) ii) a. The proportion of successes in a random sample of 400 was calculated as 50%. Estimate the population proportion with 95% confidence.

b. Repeat part (a) withp= 33%.

c. Repeat part (a) withp= 10%.

d. Discuss the effect on the width of the confidence interval estimate of reducing the sample proportion.

A) iii). Calculate the p-value of the test of the following hypotheses given thatp= .63 andn= 100:

H0: p= .60

H1: p> .60

b. Repeat part (a) with n = 200.

c. Repeat part (a) with n = 400.

d. Describe the effect on the p-value of increasing the sample size.

B) i) a. A statistics practitioner wants to test the following hypotheses:

H0:p= .70

H1:p> .70

A random sample of 100 producedp= .73.

Calculate thep-value of the test.

b. Repeat part (a) with p = .72.

c. Repeat part (a) with p = .71.

d. Describe the effect on the z-statistic and its p-value of decreasing the sample proportion.

B) ii) Determine the sample size necessary to estimate a population proportion to within .03 with 90% confidence assuming you have no knowledge of the approximate value of the sample proportion.

B) iii) Suppose that you used the sample size calculated in E) and foundp= .5.

a. Estimate the population proportion with 90% confidence.

b. Is this the result you expected? Explain

C) i) Suppose that you used the sample size calculated in Exercise E) and foundp= .75.

a. Estimate the population proportion with 90% confidence.

b. Is this the result you expected? Explain.

c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate you produced? Explain.

C) ii) Re-do Exercise E) assuming that you know that the sample proportion will be no less than .75.

C) iii) Suppose that you used the sample size calculated in Exercise H) and foundp= .75.

a. Estimate the population proportion with 90% confidence.

b. Is this the result you expected? Explain

C) iiii) Suppose that you used the sample size calculated in Exercise H) and foundp= .92.

a. Estimate the population proportion with 90% confidence.

b. Is this the result you expected? Explain.

c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate you produced? Explain.

C) iiiii) Suppose that you used the sample size calculated in Exercise H) and foundp= .5.

a. Estimate the population proportion with 90% confidence.

b. Is this the result you expected? Explain.

c. If you were hired to conduct this analysis, would the person who hired you be satisfied with the interval estimate you produced? Explain.