A researcher is interested in whether people are less able to identify emotions correctly when they are extremely tired. It is known that, using a particular method of measurement, the accuracy ratings of people in the general population are normally distributed with a mean of 85 and a variance of 18. In the present study, however, the researcher arranges to test 54 people who had no sleep the previous night. The mean accuracy for these 54 individuals was 80. Using the 0.05 level, what should the researcher conclude? Complete parts (a) through (f). (a) Carry out a Z test using the five steps of hypothesis testing. Choose a research hypothesis and a null hypothesis. Choose the correct answer below.
A. The research hypothesis is the mean of the sample population is less than the mean of the general population. The null hypothesis is the mean of the sample population is greater than or equal to the mean of the general population.
B. The research hypothesis is the mean of the sample population is greater than the mean of the general population. The null hypothesis is the mean of the sample population is equal to the general population.
C. The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same.
D. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same.
(B) Assume that the distribution of means is approximately normal. What is/are the cutoff sample score(s) on the comparison distribution at which the null hypothesis should be rejected?
(C) Determine the sample's Z score on the comparison distribution.
z=?
(D) Decide whether to reject the null hypothesis. Explain. Choose the correct answer below.
A.

B.

C. The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true.
D. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is false.
(E) Figure the 95% confidence interval.
One can be 95% confident that the true population mean is between
__ and __.
(F) Explain your answer to someone who is familiar with the general logic of hypothesis testing, the normal curve, Z scores, probability, and the idea of a distribution of means, but who has not heard of confidence intervals.
A 95% confidence interval is the range of values one can be
confident the true population mean is in this range (1,5,95, or99%). The lower limit of this interval is the mean of the (highest or lowest) distribution of means and the upper limit is the mean of the (lowest or highest) distribution of means, respectively, that would have a
99%
1%
5%
95%
chance of including the sample mean.