EXAMPLE 23 Using a confidence interval to perform two-tailed tests

In Example 14 of Chapter 8 (page 452), we found the 99% -confidence interval for , the population mean sodium content per serving of all breakfast cereals, to be the following:

Test, using level of significance , whether the population mean amount of sodium differs from the following values: (a) 100 grams, (b) 170 grams, (c) 250 grams.

Solution

The key words “differs from” mean that we are using two-tailed tests. Then, for each hypothesized value of , we determine whether it falls inside or outside the given confidence interval.

  1. The confidence interval is (144.1, 227.7), and because lies outside the interval (see Figure 33), we reject .

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  2. lies inside the interval, so we do not reject .

  3. lies outside the interval, so we reject .

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    Figure 9.40: FIGURE 33 Reject for values of that lie outside (144.1, 227.7).

NOW YOU CAN DO

Exercises 31–36.