Question

In a survey of 4074 adults, 728 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is (LL) (Round to three decimal places as needed.) nterpret your results. Choose the correct answer below. O A. With 99% confidence, it can be said that the population proportion of adults who oppose allowing transgender students to use the O B. The endpoints of the given confidence interval show that 99% of adults oppose allowing transgender students to use the bathrooms of ° C. With 99% probability, the population proportion of adults who adults who support allowing transgender students to use the bathrooms O D. With 99% confidence, it can be said that the sample proportion of adults who adults who oppose allowing transgender students to use bathrooms of the opposite biological sex is between the endpoints of the given confidence interval. the opposite biological sex. of the opposite biological sex is between the endpoints of the given confidence interval. the bathrooms of the opposite biological sex is between the endpoints of the given confidence interval

Answer 1

Solution :

Given that,

n = 4074

x = 728

Point estimate = sample proportion = $\hat p$ = x / n = 728 / 4074 = 0.179

1 - $\hat p$ = 1 - 0.179 = 0.821

At 99% confidence level the z is ,

$\alpha$ = 1 - 99% = 1 - 0.99 = 0.01

$\alpha$ / 2 = 0.01 / 2 = 0.005

Z_$\alpha$/2 = Z_0.005 = 2.576

Margin of error = E = Z_{$\alpha$ / 2} * $\sqrt$ (($\hat p$ * (1 - $\hat p$ )) / n)

= 2.576 * ($\sqrt$((0.179 * 0.821) /4074 )

= 0.015

A 99% confidence interval for population proportion p is ,

$\hat p$ - E < p < $\hat p$ + E

0.179 - 0.015 < p < 0.179 + 0.015

0.164 < p < 0.194

The 99% confidence interval for the population proportion p is : ( 0.164 , 0.194 )

option c) is correct