Question

A shipment of 500 small lab mice arrives at the animal care facility. We wish to estimate the actual mean weight of the mice. A simple random sample of 45 mice is selected and weighed, and the resulting 95% confidence interval for the actual mean weight is from 9.9 to 10.5 gram.

Using the same data to test the hypothesis about the actual mean weight, which of the following is correct at significance level alpha = 0.05?

a) We can reject the hypothesis that the true mean is 10 gram

b) We can reject the hypothesis that the true mean weight is 11 gram versus that the mean weight is not equal to 11 gram.

c) We cannot reject the hypothesis that the sample mean is 10.2

d) We cannot reject the hypothesis that 95% of individual mice weight between 9.9 and 10.5 gram.

e) None of above.

Answer 1

a) False

b) True

c) True

d) True

e) False

Explanation:

A simple random sample of 45 mice is selected and weighed, and the resulting 95% confidence interval for the actual mean weight is from 9.9 to 10.5 gram.

Any values outside the confidence interval falls in the critical region at the significance level alpha = 0.05

a) We can reject the hypothesis that the true mean is 10 gram

False. Since 10 gram is in the confidence interval given above, we cannot reject the hypothesis.

b) We can reject the hypothesis that the true mean weight is 11 gram versus that the mean weight is not equal to 11 gram.

True. Since 11 gram is outside of the confidence interval given above, we can reject the hypothesis.

c) We cannot reject the hypothesis that the sample mean is 10.2

True. Since 10.2 gram is in the confidence interval given above, we cannot reject the hypothesis.

d) We cannot reject the hypothesis that 95% of individual mice weight between 9.9 and 10.5 gram.

True. This is what 95% confidence interval suggests.