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

Question 10.83

32. Math Scores. The Institute of Educational Sciences published the results of the Trends in International Math and Science Study. In 2011, the sample mean mathematics scores for 8th-grade students from the United States and Hong Kong were 509 and 586, respectively. Suppose independent random samples are drawn from each population, and assume that the populations are normally distributed with the following summary statistics.

USA
Hong Kong

  1. Provide the point estimate of the difference in population means .

    604

  2. Calculate the margin of error for a confidence level of 90%.
  3. Construct and interpret a 90% confidence interval for .
  4. Test, at level of significance , whether .
  5. Provide two reasons why the confidence interval in (c) could not have been used to perform the hypothesis test in (d).