Question 10.141

29. Women's ownership of Businesses. Refer to Exercise 25 to answer the following questions:

  1. Construct and interpret a 90% confidence interval for the difference in population proportions.
  2. Use the confidence interval from (a) to test, using level of significance , whether the population proportions differ.
  3. Explain whether or not we could use the confidence interval from part (b) to perform the hypothesis test in Exercise 25. Why or why not?

10.3.29

(a) (–0.0745, 0.1145). TI-83/84: (–0.0749, 0.1150). We are 90% confident that the difference of the population proportion of Ohio businesses that are owned by women and the population proportion of New Jersey businesses that are owned by women lies between −0.0745(–0.0749) and 0.1145(0.1150).

(b) Our hypothesized value of 0 lies inside the interval in (a), so we do not reject . There is insufficient evidence that the population proportion of Ohio businesses that are owned by women differs from the population proportion of New Jersey businesses that are owned by women. (c) No, it is a one-sided test and confidence intervals can only be used to perform two-sided tests.