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).
lies inside the interval (11.7983, 16.2017), so we do not reject (Figure 3).
lies inside the interval, so we do not reject .
lies outside the interval, so we reject .
NOW YOU CAN DO
Exercises 27–30.