EXAMPLE 29 Using a confidence interval for to perform two-tailed hypothesis tests about

In 2013, Facebook reported that 73% of its users access Facebook using a mobile device. Suppose that a 95% confidence interval for the population of mobile accessers is (lower bound = 0.70, upper bound = 0.76). Use the confidence interval to test, using level of significance , whether the population proportion differs from

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  1. 0.69
  2. 0.72
  3. 0.77

Solution

There is equivalence between a confidence interval for and a two-tailed test for with level of significance . Values of that lie outside the confidence interval lead to rejection of the null hypothesis, whereas values of within the confidence interval lead to not rejecting the null hypothesis. Figure 41 illustrates the 95% confidence interval for .

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Figure 9.51: FIGURE 41 Reject for values that lie outside the interval (0.70, 0.76).

We want to perform the following two-tailed hypothesis tests:

To perform each hypothesis test, simply observe where each value of falls on the number line. For example, in the first hypothesis test, the hypothesized value lies outside the interval (0.70, 0.76). Thus, we reject . The three hypothesis summarized here.

Value of Form of hypothesis test,
with 		Where lies in relation
to 95% confidence
interval		 Conclusion of
hypothesis test
a. 0.69 Outside Reject
b. 0.72 Inside Do not reject
c. 0.77 Outside Reject

NOW YOU CAN DO

Exercises 23–26.