Solve the following:
Q1: 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. Describe what happens to the confidence interval estimate when the sample size increases.
Q2: a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that is 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.