We will use the process of Hypothesis testing to determine whether Shoffield should reject H_o:

            Step 1:  State the Hypothesis

                        H_o: μ ≤ 3,000

                        H_a: μ > 3,000

            Step 2:  Select Appropriate Test Statistic

Here, we have a normally distributed population with an unknown variance (we are given only the sample standard deviation) and a small sample size (less than 30.) Thus, we will use the t-statistic.

Step 3:  Specify the Level of Significance

Here, the confidence level is 90%, or 0.90, which translates to a 0.10 significance level.

Step 4:  State the Decision Rule

This is a one-tailed test. The critical value for this question will be the t-statistic that corresponds to an α of 0.10, and 14 (n-1) degrees of freedom. Using the t-table , we determine that the appropriate critical value = 1.345. Thus, we will reject the null hypothesis if the calculated test statistic is greater than 1.345.

Step 5:  Calculate sample (test) statistic

The test statistic = t = (3,150 – 3,000) / (450 / √ 15) = 1.291

Step 6:  Make a decision

Fail to reject the null hypothesis because the calculated statistic is less than the critical value. Shoffield cannot state with 90% certainty that the home game attendance exceeds 3,000.

The other statements are false. As shown above, the appropriate test is a t-test, not a Z-test. There is a test statistic for an normally distributed population, an unknown variance and a small sample size – the t-statistic. There is no test for a non-normal population with unknown variance and small sample size.