Parts a) and b) are NOT related. All are compulsory.

a) A researcher believes that the average monthly debt held by adults has changed since the onset of COVID-19. Before COVID-19, the average monthly debt per person was $350 with a standard deviation of $65. The researcher took a random sample of 36 individuals and found the average monthly debt to be $340. Assume the conditions are satisfied and do NOT need to be checked here.

i) Write the hypotheses to test the researcher's belief.

ii) Find the calculated test statistic. Show working

iii) If testing at the 10% level of significance, give the critical value.

iv) Give your DECISION, briefly explain your reasoning.

v) Is there support for the researcher's belief? Briefly explaining your reasoning.

b) You are told that the following hypotheses were used to test whether the mean weight of a part was greater than 0.10 grams.

Ho: = 0.10

Ha: > 0.10

Describe in your own words, a Type I error in this context.