Question

As part of a national sleep study, a random sample of adults was selected and surveyed about their physical activity and the number of hours they sleep each night. Among the 183 adults who exercised regularly (exercisers), 59 percent reported sleeping at least seven hours at night. Of the 88 adults who did not exercise regularly (nonexercisers), 52 percent reported sleeping at least seven hours at night. Which of the following is the most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers?

Responses:

a. Square root of the fraction with numerator 0.59 times 0.41 and denominator 183, plus the fraction with numerator 0.52 times 0.48 and denominator 88.
b. Square root of the fraction with numerator 0.59 times 0.41 plus 0.52 times 0.48 and denominator 183 plus 88.
c. Square root of 0.57 times 0.43 times (1/183 + 1/88).

Answer 1

The most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers is option a.

Step-by-step explanation:

The most appropriate standard error for a confidence interval for the difference in proportions of adults who sleep at least seven hours at night among exercisers and nonexercisers is option a.

The standard error is calculated by taking the square root of the sum of two fractions. The first fraction represents the proportion of exercisers who sleep at least seven hours, multiplied by the proportion of exercisers who don't sleep at least seven hours, divided by the sample size of exercisers.

The second fraction represents the proportion of nonexercisers who sleep at least seven hours, multiplied by the proportion of nonexercisers who don't sleep at least seven hours, divided by the sample size of nonexercisers.