Question 10.221

14. The U.S. Census Bureau reported that, for people 18 to 24 years old, the mean annual income for people who never married was $13,539 and for married people was $19,321. Suppose that this information came from a survey of 100 people from each group and that the sample standard deviations were $5000 for the people who never married and $8000 for the married people.

  1. Test, at level of significance , whether the population mean income for never-married people differs from that of married people.
  2. If we construct a 90% confidence interval for , will the interval include 0? Explain why or why not.
  3. Confirm your statements from (b).