Question 1: Suppose you draw a random sample from a population with a mean of 6 and a variance of 9. What is the standard error of the sample mean if the sample size is 49?
Question 2: Suppose you didn't know the population mean in variance from question 1, but the sample had mean 7 and variance 10. What is the estimated standard error of the sample mean?
Question 3: If you hypothesized that the mean of the population from which you drew the sample in question 2 was 8, what is the z-score of the sample mean?
Question 4: If the central limit theorem applies, what is the estimated p-value of the result found in question 3? (Use two sided test)
Question 5: Based on your previous answers, what is the lower limit of the 95% confidence interval for the sample mean.
Question 6: Now suppose the sample size were 256 and the sample mean and variance were 5.5 and 9.5 respectively. What is the estimated standard error of the sample mean?
Question 7: Based on your answer to question 6, what is the test statistic of the sample mean under the hypothesis that the population mean is 6?
Question 8: What is the p-value of the result found in question 7? (Use two sided test)
Question 9: Based on your previous answers, what is the upper limit of the 99% confidence interval for the mean.
Question 10: Now suppose you draw a sample of size 10 from a population that is known to follow a normal distribution. The sample mean is 1 and the sample variance is 3. What is the estimated standard error of the mean?
Question 11: For the sample in question 10, what is the relevant critical value (5% significance) for hypothesis tests on the mean?
Question 12: What is the test statistic for the sample in question 10 under the null hypothesis that the population mean is 0?
Question 13: If the true mean of the population from question 10 was 2, what sort of error, if any, would you make using the hypothesis test above?
Question 14: Suppose you draw a sample of size 250 from a population of size 1,000. By what factor should you adjust the standard error estimates? (Relative to the usual standard error estimator)
Question 15: To get a margin of error one-fourth as large, you would need to increase your sample size by a what factor?