You conduct a survey of a sample of 25 members of this year’s graduating marketing students and find that the average GPA is 3.2. The standard deviation of the sample is 0.4. Over the last 10 years, the average GPA has been 3.0. Is the GPA of this year’s students significantly different from the long-run average? At what alpha level would it be significant?

To determine whether the GPA of this year's students is significantly different from the long-run average, we can perform a hypothesis test using the sample data and the known long-run average.

Here are the steps to conduct a hypothesis test:

Step 1: State the null hypothesis (H0) and the alternative hypothesis (Ha).
- Null hypothesis (H0): The population mean GPA of this year's students is equal to the long-run average GPA (μ = µ0).
- Alternative hypothesis (Ha): The population mean GPA of this year's students is significantly different from the long-run average GPA (μ ≠ µ0).

Step 2: Select the appropriate test statistic and the level of significance (alpha level).
- Since we are comparing the means of two independent samples, we can use a t-test.
- The alpha level (α) represents the probability of making a Type I error, which is the rejection of a true null hypothesis. It is typically set at 0.05 (5%) or 0.01 (1%).

Step 3: Compute the test statistic.
- In this case, we need to calculate the t-score using the formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
t = (3.2 - 3.0) / (0.4 / sqrt(25))

Step 4: Determine the critical value(s).
- The critical value(s) depend on the alpha level and the degrees of freedom (df).
- Degrees of freedom (df) = sample size - 1 = 25 - 1 = 24
- We can either use the t-distribution table or statistical software to find the critical value(s) for a two-tailed test.

Step 5: Compare the test statistic to the critical value(s) and make a decision.
- If the absolute value of the test statistic is greater than the critical value(s), we reject the null hypothesis.
- If the absolute value of the test statistic is less than or equal to the critical value(s), we fail to reject the null hypothesis.

Based on the steps outlined above, we can calculate the test statistic (t) and compare it to the critical value(s) at the chosen alpha level to determine if the GPA of this year's students is significantly different from the long-run average.