Statistics question (MA 238 ASSIGNMENT)

Question

Q10. Students in MA238 spend on average 3.75 hours a week studying (with a population standard

deviation σ = 5.17).

(i) Given this fact, describe the sampling distribution of the mean if all possible random

samples of size 50 were chosen.

(ii) What can you say about the mean of all the possible sample means?

(iii) If 250 such samples were chosen at random and for each you calculated a 95% C.I for

the mean, how many such intervals would you expect to contain the true mean?

(iv) If instead you calculated a 99% C.I. for the mean, how many intervals would you now

expect to capture the true mean

Answer 1

The mean of the sampling distribution of means is the population mean: 3.75

The standard deviation of the sampling distribution of means is the population standard deviation divided by the square root of the sample size: 5.17/sqrt(50).

95% of 250 samples chosen at random would produce 95% CI that contain the true mean: 0.95 * 250

99% of 250 samples chosen at random would produce 99% CI that contain the true mean: 0.99 * 250