Example 10.2 Measuring Student Reaction to a New Textbook Hypothesis Tests for a Population Mean

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Objective To use a one-sample t test to see whether students like the new textbook any more or less than the old textbook.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Background Information n A large required chemistry course at State University has been using the same textbook for a number of years. n Over the years, the students have been asked to rate this textbook on a 1 to 10 scale, and the average rating has been stable at about 5.2. n This year, faculty decided to experiment with a new textbook. n After the course, 50 randomly selected students were asked to rate this new textbook.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Background Information -- continued n The results appear in column B of the table on the next slide. n Can we conclude that the students like this new textbook any more less than the previous textbook?

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Test of Two-Tailed Alternative

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution n The first question is whether the test should be one- tailed or two-tailed. n Of course, the faculty have chosen the new textbook with the expectation that it will be preferred by the students, but it is very possible that students will like it less than the previous textbook. n Therefore, we set this up as a two-tailed test – that is, the alternative hypothesis is that the mean rating of the new textbook is either less than or greater than the mean rating, 5.2, of the previous textbook.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution -- continued n Formally, we write the hypotheses as H 0 :  =5.2 versus H a :  5.2. n The test is run almost exactly as with a one-tailed test. We calculate the t-distributed test statistic in the same way as before. The output can be seen on the table shown earlier.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution -- continued n The p-value is then the probability beyond –1.738 in the left tail and beyond in the right tail of a t distribution with n-1=49 degrees of freedom. n The effect is to double the one-tailed p-value. From the output we see that the two-tailed p-value is n This moderately small p-value provides some evidence, but probably not convincing evidence, that the mean rating of the new textbook is different from the old mean rating of 5.2.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution -- continued n It would be more conclusive evidence if the p-value were lower. n We can now ask whether the faculty should continue to use the new textbook. n Here again, it is probably not a decision that hypothesis testing, at least by itself, should determine. n The students appear to favor the new textbook, if only by a small margin. If the faculty also favor it, we see no reason for not continuing to use it.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution -- continued n Because this is a two-tailed test, we can also perform the test by appealing to confidence intervals. n A 95% confidence for the mean rating of the new textbook was also requested in the StatPro output that was shown. n This interval extends from to Because this interval does include the old mean rating of 5.2, we cannot reject the null hypothesis at the 5% significance level.

| 10.1a | 10.3 | 10.4 | 10.5 | 10.6 | 10.7 | 10.8 | a Solution -- continued n This is in agreement with the p-value of the test, which is greater than n However, you can check that a 90% confidence interval for the mean does not include 5.2. n Therefore we can reject the null hypothesis at the 10% level. n This too is in agreement with the p-value, which is less than 0.10.