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 930 and x equals 574 who said​ "yes." Use a 99 % confidence level.

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

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

c) Construct the confidence interval. minusless than p less than minus ​(Round to three decimal places as​ needed.) ​

d) Write a statement that correctly interprets the confidence interval.

Choose the correct answer below.

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

B. One has 99​% confidence that the sample proportion is equal to the population proportion.

C. 99​% of sample proportions will fall between the lower bound and the upper bound.

D. One has 99​% 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 = 930

x = 574

a) Point estimate = sample proportion = = x / n = 574 / 930 = 0.617

1 - = 1 - 0.617 = 0.383

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 (((0.617 * 0.383) / 930 )

= 0.041

c) A 99% confidence interval for population proportion p is ,

- E < p < + E

0.617 - 0.041 < p < 0.617 + 0.041

( 0.576 < p < 0.658 )

d) D. One has 99​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion