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 equals n=1065 and x equals 548 who said​ "yes." Use a 95 confidence level.

a) Find the best point estimate of the population proportion p. Round to three decimal places as​ needed.)

b) Identify the value of the margin of error E. E = (Round to three decimal places as​ needed.)​

​c) Construct the confidence interval < p <. ​(Round to three decimal places as​ needed.)

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

A.One has 9999​% confidence that the sample proportion is equal to the population proportion.

B.There is a 9999​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

C.One has 9999​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.Your answer is correct.

D. 9999​% of sample proportions will fall between the lower bound and the upper bound.

Answer 1

Solution :

Given that,

n = 1065

x = 548

Point estimate = sample proportion = = x / n = 548 / 1065 = 0.515

1 - = 1 - 0.515 = 0.485

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

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

= 2.576 * (((0.515 * 0.485) / 1065)

= 0.030

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.515 - 0.030 < p < 0.515 - 0.030

0.485 < p < 0.545

B.There is a 99% chance that the true value of the population proportion will fall between the lower bound and the upper bound.