Question

Do one of the following, as appropriate: (a) Find the critical value zα/2 (b) find the critical value tα/2, (c) state that neither the normal nor the t distribution applies. 90% confidence interval for μ; n = 9; σ = 4.2, population appears to be very skewed.

Answer 1

For a 90% confidence interval with a small sample size and a skewed population, we should use the t-distribution to find the critical value. Looking up the critical value in the t-distribution table, we find it to be approximately 2.306.

Step-by-step explanation:

To find the critical value for a 90% confidence interval, we need to determine whether to use the z-distribution or the t-distribution. The population is said to be very skewed, which suggests that the normal distribution might not be appropriate. Since the sample size is small (n = 9), we can use the t-distribution. The critical value tα/2 can be found by referring to the t-distribution table with n-1 degrees of freedom and α = (1 - confidence level) / 2. In this case, α = (1 - 0.90) / 2 = 0.05 / 2 = 0.025. Looking up this value in the t-distribution table with 9-1 = 8 degrees of freedom, we find