The National AIDS Behavioral Surveys interviewed a sample of adults in cities where AIDS is most...

The National AIDS Behavioral Surveys interviewed a sample of adults in cities where AIDS is most common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 803 from the population of all heterosexuals in high-risk cities who have multiple partners. These people risk infection with the AIDS virus. Yet 304 of the respondents said they never use condoms.

Find a 95% confidence interval for the population proportion that never use condoms?

Solutions

Expert Solution

Solution :

Given that,

n = 803

x = 304

Point estimate = sample proportion = = x / n = 304/803=0.379

1 - = 1- 0.379 =0.621

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * $\sqrt$ ((( * (1 - )) / n)

= 1.96 ( $\sqrt$ ((0.379*0.621) /803 )

E = 0.0336

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.379-0.0336 < p <0.379+ 0.0336

0.3454< p < 0.4126

The 95% confidence interval for the population proportion p is : 0.3454, 0.4126

orchestra answered 1 year ago

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