For Exercises 15–18, do the following:

  1. Check the normality conditions.
  2. State the hypotheses.
  3. Find and the rejection rule.
  4. Calculate .
  5. Compare with . State the conclusion and the interpretation.

Question 9.281

15. Test whether the population proportion is less than 0.5. A random sample of size 225 yields 100 successes. Let level of significance .

9.5.15

(a) We have and , so we can use thetest for proportions. (b) (c) . Reject if . (d) −1.67 (e) Since , we reject . There is evidence that the population proportion is less than 0.5.