Question

How Important Is Regular Exercise? In a recent poll1 of 1000 American adults, the number saying that exercise is an important part of daily life was 753. Use StatKey or other technology to find a 90% confidence interval for the proportion of American adults who think exercise is an important part of daily life. Click here to access StatKey. Round your answer to three decimal places. The 90% confidence interval is Enter your answer; the 90% confidence interval, value 1

Answer 1

Explanation:

Given that in a recent poll 1 of 1000 American adults, the number saying that exercise is an important part of daily life was 753.

Sample proportion =
`(753)/(1000) =0.753`

To find 90% confidence interval we must find std error of proportion first

As per central limit theorem, sample proportion will follow a normal distribution with mean = 0.753

Std error of proportion=
`√(0.753*0.247/1000) \\=0.01363`

90% Z critical value = 1.645

Margin of error = 1.645*0.01363 = 0.0224

Confidence interval lower bound = 0.753-0.0224=0.731

Upper bound = 0.775