Question

you have a sample drawn from i.i.d. normal random variables, and the sample size is 15. if you are interested in forming an 80% confidence interval for the population average, what critical value would you use?

Answer 1

To form an 80% confidence interval for the population average (mean) with a sample size of 15, we need to determine the critical value associated with an 80% confidence level.

Since the sample is drawn from independent and identically distributed (i.i.d.) normal random variables, we can use the t-distribution for small sample sizes. The critical value is based on the degrees of freedom, which is equal to the sample size minus 1 (n-1).

For an 80% confidence interval, we need to find the critical value that leaves 10% of the probability in each tail of the t-distribution. This means we have 5% in the left tail and 5% in the right tail.

Using a t-table or statistical software, we can find the critical value associated with a 5% tail probability and 14 degrees of freedom (15-1). For an 80% confidence interval, the critical value is approximately 1.761.

Therefore, to form an 80% confidence interval for the population average with a sample size of 15, we would use a critical value of 1.761.