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.
The confidence interval is (144.1, 227.7), and because lies outside the interval (see Figure 33), we reject .
535
lies inside the interval, so we do not reject .
lies outside the interval, so we reject .
NOW YOU CAN DO
Exercises 31–36.