For Exercises 29–49, assume normality and use Welch's test and interval unless otherwise indicated.

Question 10.82

31. Income in California Counties. According to random samples taken in 2010 by the Bureau of Economic Analysis, the mean income for Sacramento County and Los Angeles County, California, was $31,987 and $33,179, respectively. Suppose the samples had the following sample statistics.

Sacramento County
los Angeles County
  1. Provide the point estimate of the difference in population means .
  2. Calculate the margin of error for a confidence level of 95%.
  3. Construct and interpret a 95% confidence interval for .
  4. Test, at level of significance , whether .
  5. Explain whether the confidence interval in (c) could have been used to perform the hypothesis test in (d). Why or why not?

10.2.31

(a) –$1192 (b) $2426.7954 (c) (–3618.7954, 1234.7954). We are 95% confident that the difference in population mean incomes lies between –$3618.7954 and $1234.7954. (d) versus . Reject if the . ; (TI-84: 0.1608312442). The is not , so we do not reject . There is insufficient evidence at level of significance that the population mean income of Sacramento County is less than that of Los Angeles County. (e) No. The hypothesis test in (d) is a one-tailed test and confidence intervals can only be used for two-tailed tests.