Question: Sam claims that the true mean price for a Sydney to Osaka economy-class airline ticket is in excess of $800. You wish to test this claim, so you randomly sample 20 Sydney to Osaka economy-class ticket sales and record the following:

Average price for the sample = $830

Sample standard deviation = $80

(a) State the null and alternate hypotheses.

(b) Test whether Sam is correct at the 5% significance level.

(c) What is the probability of a Type I error in the test conducted in (b)?