For Exercises 49–56, do the following:

  1. State the hypotheses.
  2. Find and the critical region.
  3. Find . Also, draw a standard normal curve showing , the critical region, and .
  4. State the conclusion and the interpretation.

Question 9.86

51. Text Messages. The Pew Internet and American Life Project reports that young people ages 12–17 send a mean of 60 text messages per day. A random sample of 100 young people showed a mean of 69 text messages per day. Assume . Test, using level of significance , whether the population mean number of text messages per day differs from 60.

9.2.51

(a) (b) . Reject if or (c)

image

(d) is . Therefore we reject . There is evidence at level of significance that the population mean number of text messages sent per day for young people ages 12–17 differs from 60.