Section 2: Hypothesis Testing

Question 1

The admissions officer for the graduate programs at the University of Adelaide believes that the average score on an exam at his university is significantly lower than the national average of 1300. Assume that the population standard deviation is 125 and that a random sample of 25 scores had an average of 1275.

a. State the appropriate null and alternative hypotheses. Explanation to be provided.

b. Explain the risks associated with Type 1 and Type 2 errors in this context.

Question 2

Last season the mean amount spent in a store per customer was $41.76 with a population standard deviation of $17.05. The store manager wishes to determine at 5% level of significance if the sales for the current season have changed compared to last season. This season the standard deviation for all sales can be assumed to be the same as last season. The manager takes a sample of 75 customers, finding a mean of $43.19.

1. Determine, using the critical value approach, whether themean amount spent this seasonhas changed compared to last season. Interpret the result.
2. Find the p-value for the test and explain how the p-value relates to your conclusion in part b). Interpret the result.