EXAMPLE 18 interval for the population proportion

Using the Starbucks' data from Example 17, (a) verify that the conditions for constructing the interval for have been met, and (b) construct a 95% confidence interval for the population proportion of all Starbucks' transactions that are made using a cell phone.

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Solution

  1. We have transactions and . We check the conditions for the confidence interval. There are successes, which is ≥5, and there are failures, which is also ≥5. The conditions for constructing the interval for have been met.
  2. From Table 1, the confidence level of 95% gives . Thus, the confidence interval is

We are 95% confident that the population proportion of Starbucks' sales transactions made using a cell phone lies between 0.0412 and 0.1588. (See Figure 27.)

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Figure 8.27: FIGURE 27 95% Confidence interval for the population proportion of Starbucks' sales transactions made using a cell phone.

NOW YOU CAN DO

Exercises 7–20.