1. What is the difference between a one-tail test and a two-tail test?
2. What is meant by a p-value?
3. If, in a sample of n = 16 selected from a normal population, ????? = 56 and S = 12, what is the value of tSTAT if you are testing the null hypothesis ????0: ???? = 50?
4. In problem 9.18, how many degrees of freedom does the t test have?
5. In problems 9.18 and 9.19, what are the critical values of t if the level of significance (α) is 0.05 and the alternative hypothesis is ????1: ???? ≠ 50?
6. In problems 9.18 - 9.20, what is your statistical decision is the alternative hypothesis is ????1: ???? ≠ 50?
7. One operation of a steel mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw and requires the resulting parts must be cut to within ±0.005 inch of the length specified by the automobile company. The file steel contains a sample of 100 steel parts. The measurement reported is the difference, in inches, between the actual length of the steel part, as measured by a laser measurement device, and the specified length of the steel part. For example, a value of -0.002 represents a steel part that is 0.002 inch shorter than the specified length.
a) At the 0.05 level of significance, is there evidence that the mean difference is not equal to 0.0 inches? b) Construct a 95% confidence interval estimate of the population mean. Interpret this interval.
c) Compare the conclusions reached in (a) and (b).
d) Because n = 100, do you have to be concerned about the normality assumption needed for the t test and t interval?
8. In a one-tail hypothesis test where you reject H0 only in the upper tail, what is the p-value if ZSTAT = +2.00?
9. In problem 8, what is your statistical decision if you test the null hypothesis at the 0.05 level of significance?
10. In a one-tail hypothesis test where you reject H0 only in the lower tail, what is the pvalue if ZSTAT = -1.38? 9.39: In problem 9.38, what is your statistical decision if you test the null hypothesis at the 0.01 level of significance?
11. A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 50 nonprofit organizations, the mean onetime gift donation in the past year was $62, with a standard deviation of $9.
a) If you test the null hypothesis at the 0.01 level of significance, is there evidence that the mean one-time gift donation is greater than $60?
b) Interpret the meaning of the p-value in this problem.