1)

In the library on a university campus, there is a sign in the elevator that indicates a limit of 50 persons. Furthermore, there is a weight limit of 8000 pounds. Suppose that the average weight of students, faculty, and staff on campus is 147 pounds, that the standard deviation is 30 pounds. You want to estimate the chance that a random sample of 50 persons on the elevator will exceed the weight limit of 8000 pounds by using z-scores and the standard normal distribution. Is it necessary to assume that the weights of individuals on campus is at least approximately normally distributed?

Read carefully and select one of the following:

a) Yes, otherwise the population could be skewed.

b) No, since the population is normally distributed for a large sample.

c) Yes, otherwise the sampling distribution of the sample means is not most likely normally distributed.

d) No, since the sampling distribution of the sample means is approximately normally distributed for a large sample.

2).

The National Cancer Institute conducted a 2-year study to determine whether cancer death rates for areas near nuclear power plants are higher than for areas without nuclear facilities. A spokesperson for the Cancer Institute said, "From the data at hand, there was no convincing evidence of any increased risk of death from any of the cancers surveyed due to living near nuclear facilities." (1 points for each)

A. Let p denote the proportion of the population in areas near nuclear power plants who die of cancer during a given year. The researchers at the Cancer Institute have considered the null and alternative hypotheses below:

H0: p = value for areas without nuclear facilities

Ha: p > value for areas without nuclear facilities According to the spokesperson's statement, what is the conclusion of the National Cancer Institute? Select one of the following:

a) Reject H0 b) Fail to reject H0 c) Reject Ha d) Fail to reject Ha

B. If the National Cancer Institute researchers were incorrect in their conclusion that there is no increased cancer risk associated with living near a nuclear power plant, are they making a Type I or a Type II error? Read carefully and select one of the following:

a) A Type II error, if the researchers were incorrect in their conclusion this would be rejecting the null hypothesis when the null hypothesis is true.

b) A Type I error, if the researchers were incorrect in their conclusion this would be failing to reject the null hypothesis when the null hypothesis is true.

c) A Type II error, if the researchers were incorrect in their conclusion this would be failing to reject the null hypothesis when the null hypothesis is false.

d) A Type I error, if the researchers were incorrect in their conclusion this would be rejecting the null hypothesis when the null hypothesis is false.