Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n = 1049 and x = 510 who said​ "yes." Use a 95% confidence level.

​a) Find the best point estimate of the population proportion p.

Answer 1

Solution :

Given that,

a)

Point estimate = sample proportion = = x / n = 510 / 1049 = 0.486

1 - = 1 - 0.486 = 0.514

Z/2 = 1.96

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

= 1.96 * (((0.486 * 0.514) / 1049)

Margin of error = E = 0.030

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.486 - 0.030 < p < 0.486 + 0.030

0.456 < p < 0.516

The 95% confidence interval for the population proportion p is : 0.456 , 0.516