EXAMPLE 10 Using a confidence interval to perform a two-tailed test about

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Use the 90% confidence interval for the difference in population mean credit scores from Example 9 to test, using level of significance , whether differs from the following values:

  1. 60
  2. 70

596

Solution

The hypotheses for our two-sample test look like this:

which is equivalent to the following, if we subtract from each side of the equations:

  1. Here, we replace zero with the value of 60 hypothesized for the difference in population means, obtaining

    The value of 60 lies outside the confidence interval (60.066, 85.934) from Example 9; therefore, we reject .

  2. Our hypotheses are

    The value of 70 lies inside the confidence interval (60.066, 85.934); therefore, we do not reject .

NOW YOU CAN DO

Exercises 17–20.