Question

In a survey of

2231

adults in a recent​ year,

1438

say they have made a New​ Year's resolution.

Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.

The​ 90% confidence interval for the population proportion p is

left parenthesis nothing comma nothing right parenthesis,.

​(Round to three decimal places as​ needed.)

Answer 1

Sample proportion = 1438 / 2231 = 0.645

90% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.645 - 1.645 * sqrt( 0.645* 0.355 / 2231) < p < 0.645 + 1.645 * sqrt( 0.645* 0.355 / 2231)

0.628 < p < 0.662

90% CI is ( 0.628 , 0.662 )

Interpretation -

We are 90% confident that population proportion falls between 0.628 and 0.662

90% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ​​​​​​​ ) / n)

0.645 - 1.96 * sqrt( 0.645* 0.355 / 2231) < p < 0.645 + 1.96 * sqrt( 0.645* 0.355 / 2231)

0.625 < p < 0.665

95% CI is ( 0.625 , 0.665 )

We are 90% confident that population proportion falls between 0.625 and 0.665