For Exercises 23–25, do the following:

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

Question 9.410

25. Test whether the population proportion is not equal to 0.4. A random sample of size 100 yields 55 successes. Let . For Exercises 26 and 27, do the following:

  1. Check the normality conditions.
  2. State the hypotheses and the rejection rule for the -value method, using level of significance .
  3. Calculate .
  4. Calculate the -value.
  5. State the conclusion and the interpretation.

9.99.25

(a) We have and . (b) (c) . Reject if or . (d) (e) Since , we reject . There is evidence that the population proportion is not equal to 0.4.