The Vice-Chancellor of the University of the Sunshine Coast claimed that the average cost of rental accommodation in the area close to campus was $140 per week. The Student Guild, being sceptical about the validity of this claim, took a random sample of 45 quotes and found that the average rental was $147.80 per week. On the basis of advice given to them by a local real estate agent, it could be assumed that the standard deviation of rental prices in the area was $25.00 per week.

1. State the direction of the alternative hypothesis used to test the Vice-Chancellor's claim. (Options are greater than, greater than or equal to, less than, less than or equal to or finally not equal to)

2. Use the tables in the text to determine the critical value used to conduct the test, assuming a 10% level of significance. If there are two critical values, state only the positive value.

3. Calculate the test statistic, reporting your answer to two decimal places.

4. Is the null hypothesis rejected for this test? yes or no.

5. If it is shown later that the average rental price is $145 per week, determine the nature of the decision made in the test. Was the correct decision made, a Type I error made or a Type II error made?

6. Regardless of your answer for 4, if the null hypothesis was rejected, could we conclude that the Vice-Chancellor's claim is valid? yes or no