For Exercises 51–58, do the following:

  1. State the hypotheses and the rejection rule.
  2. Calculate .
  3. Find the -value.
  4. State the conclusion and the interpretation.

Question 9.161

55. Millennials' Income. The Pew Research Center reported in 2014 that Millennials (those ages 25–32) with Bachelor's degrees working full time are making on average $17,500 more per year than those Millennials with only a high school education ($45,500 vs. $28,000). Suppose that, in a random sample of 36 Millennials with Bachelor's degrees taken today, the sample mean income is $50,000. Assume . Test whether the population mean annual income has increased from its previous value of $45,500 using level of significance .

9.3.55

(a) . We will reject if the . (b) (c) (d) The is not . Therefore we do not reject . There is insufficient evidence at level of significance that the population mean annual income of Millennials with Bachelor's degrees working full time has increased from $45,500.