Answer to Question #98711 in Statistics and Probability for Juliet Beglaryan

Question

Question #5 An random sample of 20 third-grade children is selected and each is given a test to measure their reading ability. We are interested in a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points and the standard deviation is 12 points. Obtain a 90% CI for the population mean score of third graders (use t* = 1.729).
Question #6You are thinking of using a t procedure to construct a 95% confidence interval for the mean of a population. You suspect the distribution of the population is not Normal and may be skewed.Which of the following statements is correct?a. You should not use the t procedure since the population does not have a Normal distribution.b. You may use the t procedure, provided your sample size is large, say at least 50.c. You may use the t procedure since it is robust to non-Normality.

Answer 1

Question #5

The margin of error associated with the confidence interval is

$$t_{(20-1)}\cdot{s \over \sqrt{n}}$$

Given that

$$t_{(20-1)}=t^*=1.729, s=12, n=20$$

$$margin\ of\ error=1.729\cdot{12\over \sqrt{20}}\approx4.64$$

Question #6

The t procedures can be used even for clearly skewed distributions when the sample is large, roughly n ≥ 40 (or 50). 

Correct answer

b. You may use the t procedure, provided your sample size is large, say at least 50.