Mean Family Size. Use the following information for Exercises 72–74: According to the Statistical Abstract of the United States, the mean family size in 2010 was 3.14 persons, reflecting a slow decrease since 1980, when the mean family size was 3.29 persons. Has this trend continued to the present day? Suppose a random sample of 225 families taken this year yields a sample mean size of 3.05 persons, and suppose we assume that the population standard deviation of family sizes is 1 person.

Question 9.179

73. Refer to Exercise 72.

  1. What is the smallest -value for which you will reject ?
  2. Which type of error is it possible that we are making—a Type I error or a Type II error? Which type of error are we certain we are not making?
  3. Suppose a newspaper headline referring to the study was “Mean Family Size Decreasing.” Is the headline supported or not supported by the data and the hypothesis test?

9.3.73

(a) 0 (b) Type II error; Type I error (c) This headline is not supported by the data and our hypothesis test.