Question

A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n=941 and x=542 who said​ "yes." Use a 90% confidence level.

1. Find the best point estimate of the population proportion p. (round to three decimal places as needed)

2. Identify the value of the margin of error E (round to three decimal places as needed)

3. Construct the confident interval __< p < __

4. write a statement that correctly interprets the confidence interval. Choose the correct answer below.

a. one has 90% of confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

b. one has 90% that the sample proportion is equal to the population proportion.

c. there is a 90% chance that the true value of the population proportion will fall between the lower bound and upper bound

d. 90% of sample proportion will fall between the lower bound and the upper bound

Answer 1

Solution :

Given that,

1) Point estimate = sample proportion = = x / n 542 / 941 = 0.576

1 - = 1 - 0.576 = 0.424

Z/2 = Z0.05 = 1.645

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

= 1.645 (((0.576 * 0.424) / 941)

= 0.027

3) A 90% confidence interval for population proportion p is ,

- E < p < + E

0.576 - 0.027 < p < 0.576 + 0.027

( 0.549 < p < 0.603 )

4) a. one has 90% of confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.