EXAMPLE 6 Using a interval for to perform tests about

Example 5 provided a 95% confidence interval for the population mean of the differences between quiz scores before and after visiting the Math Center as (11.7983, 16.2017). Test, using level of significance , whether the population mean of the differences between quiz scores before and after visiting the Math Center differs from these values: (a) 15 points, (b) 16 points, (c) 17 points.

584

Solution

We state the hypotheses and determine if each proposed value lies inside or outside of the confidence interval (11.7983, 16.2017).

  1. lies inside the interval (11.7983, 16.2017), so we do not reject (Figure 3).

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

  3. lies outside the interval, so we reject .

    image
    Figure 10.3: FIGURE 3 Reject for values of that lie outside the confidence interval.

NOW YOU CAN DO

Exercises 27–30.