An astronomer is testing the claim that the mean brightness of a certain star is now more than 30 units. The astronomer is able to get 6 readings on the star during an experiment as shown in the table. Using a 1% level of significance, does this indicate a new mean brightness of more than 30?

Reading Brightness

1 30

2 30

3 29

4 31

5 32

6 33

a. State the null and alternative hypotheses.

b. Calculate the expected results for the hypothesis test assuming the null hypothesis is true and determine the hypothesis test model, i.e., "cut-off" critical values etc.

c. Formulate the decision rule, i.e., include "one-tail" left, or "one-tail" right, or "two-tail" determination etc.

d. Determine the experimental outcome.

e. Determine the conclusion, and answer the question(s) posed in the problem, if any.

(Please Include Graph)