Suppose you draw a random sample from a population

Suppose you draw a random sample from a population

Subject: Economics / General Economics
Question
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?