Question: A) a. A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample

A) a. A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample mean to be 100. Estimate the population mean with 90% confidence.

b. Repeat part (a) using a 95% confidence level.

c. Repeat part (a) using a 99% confidence level.

d. Describe the effect on the confidence interval estimate of increasing the confidence level.

B) a. The mean of a random sample of 25 observations from a normal population with a standard deviation of 50 is 200. Estimate the population mean with 95% confidence.

b. Repeat part (a) changing the population standard deviation to 25.

c. Repeat part (a) changing the population standard deviation to 10.

d. Describe what happens to the confidence interval estimate when the standard deviation is decreased.

C) a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean.

b. Repeat part (a) with a sample size of 100.

c. Repeat part (a) with a sample size of 400.

D) a. Given the following information, determine the 98% confidence interval estimate of the population mean:

x bar= 500 = 12 n = 50

b. Repeat part (a) using a 95% confidence level.

c. Repeat part (a) using a 90% confidence level.

d. Review parts (a)-(c) and discuss the effect on the confidence interval estimator of decreasing the confidence level.

E) a. The mean of a sample of 25 was calculated asx bar= 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence.

b. Repeat part (a) changing the population standard deviation to 30.

c. Repeat part (a) changing the population standard deviation to 60.

d. Describe what happens to the confidence interval estimate when the standard deviation is increased.

F) a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found thatis xbar=10. Estimate the population mean with 90% confidence.

b. Repeat part (a) with a sample size of 25.

c. Repeat part (a) with a sample size of 10.

d. Describe what happens to the confidence interval estimate when the sample size decreases.

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