Question: Sally claims that the true mean price for a Sydney to Singapore economy class airline ticket $1000. The population standard deviation is $200. You wish to test this claim, so you randomly sample 20 Sydney to Singapore economy-class ticket sales and record the following:

Average price for the sample = $880

(a) State the null and alternate hypotheses.

(b) Assuming the true average Sydney to Singapore economy-class airline ticket price is $1100 and the population standard deviation is $260, calculate the probability of a Type II error when testing (a) at the 5% significance level.

(c) Assuming the true average Sydney to Singapore economy-class airline ticket price is $1060 and the population standard deviation is $260, calculate the probability of a Type II error when testing (a) at the 5% significance level.

(d) What is the relation between the power of the test and the distance of the true population mean from the hypothesised mean?