Question1

It is known that the time to complete a certain task at the manufacturing process is normally distributed with a mean of 35 minutes. If a random sample of 20 workers has the average time of 33.1 minutes to complete the task with the standard deviation of 4.3 minutes, test the hypothesis, at the 0.05 level of significance, that = 35 minutes against the alternative that < 35 minutes. Show all our work.

Question2

According to a dietary study, high sodium intake may be related to ulcers, stomach cancer and migraine headaches. The human requirement for salt is only 220 milligrams per day, which is surpassed in most single servings of ready-to-eat cereals If a random sample of 20 similar serings of a certain cereal has a mean sodium content of 244 milligrams and a standard deviation of 24.5 milligrams, does this suggest at the 0.05 level of significance that the average sodium content for a single serving of such cereal is greater than 220 milligrams. Assume the distribution of sodium contents to be normal. Show all your work.