1. You work for a charitable organization and you want to estimate the average age of the people who donate to your organization. You get a random sample of n = 120 donors and the value of the sample mean is 42 years. The value of the sample standard deviation is 19 years.
The lower and upper end of the 95% confidence interval for the average age of people who donate to your organization are:
a [36.4, 47.6]
b [37.5, 46.5]
c [38.6, 45.4]
d [39.8, 44.2]
2. In the previous question you want to test the hypothesis, at the 5 percent level of significance, that the average age is at least 45 years. Compute the probability value for the test.
a 0.042 Reject the null hypothesis and conclude the mean age is less than 45.
b 0.042 Do not reject the null hypothesis. Conclude the mean age is not less than 45.
c 0.004 Reject the null hypothesis and conclude the mean age is less than 45.
d 0.004 Do not reject the null hypothesis. Conclude the mean age is not less than 45.
3. Regardless how you answered the previous question, which of the following statements is correct?
a If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type II error.
b If the mean age is in fact greater than 45 and the hypothesis test leads you to conclude that it is less than 45, the you have committed a Type I error.
c If the mean age is less than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type I error.
d If the mean age is in at least than 45 and the hypothesis test leads you to conclude that it is greater than 45, the you have committed a Type II error.
4. You are reading a report that contains a hypothesis test you are interested in. The writer of the report writes that the p-value for the test you are interested in is 0.091, but does not tell you the value of the test statistic. From this information you can:
a You cannot decide based on this limited information. You need to know the value of the test statistic.
b Not reject the hypothesis at a Probability of Type I error = 0.10, and not reject at a Probability of Type I error = 0.05
c Reject the hypothesis at a Probability of Type I error = 0.10, and reject at a Probability of Type I error = 0.05
d Reject the hypothesis at a Probability of Type I error = 0.10, but not reject at a Probability of Type I error = 0.05