1) In a certain country, it is claimed that the mean height of men is 169cm. I take a random sample of 45 men in this country and find an average height of 173cm and a standard deviation of 7cm. Suppose this country has over a million men. Determine, with 95% confidence, if we can reject the claimed mean and accept that the population mean height of men in this country is greater than 169cm.
2) I claim that at least 50% of first-year statistics students in Canada enjoy math (consider this the null hypothesis). However, you take a random sample of 50 statistics students in Canada and find that only 39% claim to enjoy math. Determine with 99.5% confidence if you can reject the null hypothesis and accept that the population proportion is less than 50%.
3) Suppose that the mean grade (out of 100) on all final exams at U of Toronto is claimed to be 65 with a known standard deviation of 14. However, you take a random sample of 75 final exams and find that the mean grade (out of 100) is 61. Determine with 99% confidence if you can reject the claimed mean and accept that the population mean grade (out of 100) on all final exams at U of Toronto is not equal to 65%. You can assume that over 10,000 exams have been written at U of Toronto.