Is it significant? Over several years and many thousands of students, 89% of the high school students in a large city have passed the competency test that is one of the requirements for a diploma. Now reformers claim that a new mathematics curriculum will increase the percentage who pass. A random sample of 1000 students follow the new curriculum. The school board wants to see an improvement that is statistically significant at the 5% level before it will adopt the new program for all students. If p is the proportion of all students who would pass the exam if they followed the new curriculum, we must test H0: p = 0.89 Ha: p > 0.89

(a) Suppose that 906 of the 1000 students in the sample pass the test. Show that this is not significant at the 5% level. (Follow the method of Example 3, page 490, in Chapter 22.)

(b) Suppose that 907 of the 1000 students pass. Show that this is significant at the 5% level.

(c) Is there a practical difference between 906 successes in 1000 tries and 907 successes? What can you conclude about the importance of a fixed significance level?