Q1. An IDS student executed a regression to predict the average GPAs (the dependent variable, or Y) using the number of attendances (the independent variable, or X). The students expected that as the number of attendances increases the GPA increases.

a.State Ho and Ha with regards to 1:

Ho:

Ha:

b. The standard deviation of Y is 22. The square root of the sum of the squared residuals divided by n-2 equals 11. Does this suggest that the regression fits the data well? (No explanation required.) Yes orNo

Q2. The student executes a hypothesis test with an alpha = 5% and rejects Ho for Ha.

a. What is the probability that the statistical conclusion is wrong?

b. If the student executed the same hypothesis test (with the above alpha) on different random samples of data 2,100 times, approximately how many times would it make the mistake of rejecting Ho when Ho is actually true in the population? Show your calculation below:

Q3. A population distribution has a symmetric shape.

a. What would be the shape of the sampling distribution?

b. The size of the samples used to build the three sampling distributions are 27, 42, and 52. Which one of these sample sizes has the tightest sampling distribution?