Question 1: (3 marks) A psychologist has to develop a new test of spatial perception, and she wants to estimate the mean score achieved by male pilots. How many people must she test if she wants the sample mean to be in error by no more than 2.0 points, with 95% confidence? An earlier study suggests that= 24.3.

Question 2: (3 marks) A random sample of 25 Ontario households using natural gas heating show that the mean monthly consumption of natural gas is 107.73 cu. ft., with a standard deviation of 13.94 cu. ft. Use these statistics to construct a 95% confidence interval for the mean monthly consumption for the population of all Ontario households.

Question 3: (3 marks) In a study relating the amounts of time required for room service delivery at a newly openedRadissonHotel, 20 deliveries had a mean time of 24.2 min and a standard deviation of 8.7 min. The sample data appears to have a bell-shaped distribution. Find the 90% confidence interval for the mean time of all deliveries.

Question 4: (5marks)

In a study of distancestravelledby buses before the first major engine failure, a sampling of 60 buses resulted in a mean of 152,600 km. This means that our sample had their first major engine failure at an average of 152,600 km. At the 0.05 level of significance, test the manufacturers claim that mean distancetravelledbefore a major engine failure is more than 154,000 km. From previous research we know the populationstandard deviation is 6400 km.

Question 5: (5 marks) A night time cold medicine bears a label indicating the presence of 600 mg of acetaminophen in each fluid ounce of the drug. From previous studies the populationstandard deviation is known to be 21 mg.Suppose that Health Canada randomly selected 153 one-ounce samples and found that the mean acetaminophen content was 589 mg. Using, test the claim of the pharmaceutical company that the population mean is different from 600 mg. Would you buy this cold medicine?Give your reasons.

Question 6: (5 marks) The expense of moving the storage yard for the Consolidated Package Delivery Service (CPDS) is justified only if it can be shown that the daily mean travel distance will be significantly reduced from 342 km. In trial runs of 12 delivery trucks, the mean and standard deviation are found to be 318 km and 67 km, respectively. At the 0.01 level of significance, test the claim that the mean is less than 342 km. Should the storage yard be moved? Give your reasons.