Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll of 968 randomly selected American adults, 511 of them responded with “yes.”

a). Find the 95% confidence interval for the proportion of adults who felt vulnerable to identify theft .

b). Write a statement that correctly interprets the confidence interval. Choose the correct answer below.

A. One has 95% confidence that the sample proportion is equal to the population proportion.

B. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Answer 1

Solution :

Given that,

n = 968

x = 511

Point estimate = sample proportion = = x / n = 511/968=0.528

1 -   = 1- 0.528 =0.472

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    * ((( * (1 - )) / n)

= 1.96 (((0.528*0.472) /968 )

= 0.0314

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.528-0.0314 < p < 0.528+0.0314

0.4966< p < 0.5594

The 95% confidence interval for the population proportion p is : 0.4966,0.5594

correct option B. One has 95% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.