1 we conduct a hypothesis test of H0: = 180 vs Ha: > 180 to determine whether the true mean height of all MLB players is greater than 180 cm. The mean height of random sample of 25 major league baseball (MLB) players is calculated to be 183 cm. The P- value of the test is calculated to be 0.02. What is the correct interpretation of this P- value?

a the probability that the true mean height of all MLB players is greater than 180 cm 0.02

b given that the sample mean height is 183, the probability that the true mean height of all MLB players is greater than 180 cm 0.02

c if we took repeated samples of 25 MLB players and conducted that test in a similar manner, 2% of all samples would have means at least as high as 180 cm.

d if the true mean height of all MLB players was 180cm, the probability of rejecting the null hypothesis would 0.02

e if the true mean height of all MLB players was 180cm, the probability of observing a sample mean at least as high as 183 cm would be 0.02.

2 A test H0: = 800 vs Ha: 800 is conducted for the mean of some normally distributed variable. We take a random sample of ten individuals and calculate a sample mean of 850. A 96% confidence interval is calculated to be (798,902). which of the following statement is true?

a we fail to reject H0 at the level 4% level significance, because 850 is contained in the 96% confidence interval.

b we fail to reject H0 at the level 4% level significance, because 800 is contained in the 96% confidence interval.

c we reject H0 at the level 4% level significance, because 800 is contained in the 96% confidence interval.

d we fail to reject H0 at the level 8% level significance, because 850 is contained in the 96% confidence interval.

e we fail to reject H0 at the level 8% level significance, because 800 is contained in the 96% confidence interval.

3 Suppose that IQs of adult Canadians follow a normal distribution with the unknown standard deviation. A researcher takes a random sample of 25 adult Canadians who have mean IQ of 116 and a standard deviation of 12

if the researcher believes that the true mean IQ of adult Canadians is greater than 110, then what is the P- value for the appropriate test of significance?

a between 0.0025 and 0.005

b between 0.005 and 0.01

c between 0.01 and 0.02

d between 0.02 and 0.04

4 A machine fills boxes of cereal in a factory. The average weight of cereal in a random sample of 17 boxes is calculated to be 350 grams and the sample standard deviation is calculated to be 8 grams. Weights of cereal per box are known to follow a normal distribution. We can a 95% confidence interval for the true mean weight of cereal per box. The margin of error for the appropriate confidence interval is:

a 3.71

b 3.51

c 3.31

d 3.91

e 4.11