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 923n=923

and

x equals 554x=554

who said​ "yes." Use a

99 %99%

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.

Eequals=

​(Round to three decimal places as​ needed.)

​c) Construct the confidence interval.

nothingless than p less than<p<nothing

​(Round to three decimal places as​ needed.)

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

A.

9999​%

of sample proportions will fall between the lower bound and the upper bound.

B.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.

C.One has

9999​%

confidence that the sample proportion is equal to the population proportion.

D.There is a

9999​%

chance that the true value of the population proportion will fall between the lower bound and the upper bound.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 554 / 923 = 0.600

Z_/2 = 2.576

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

= 2.576 * (((0.600 * 0.400) / 923)

= 0.042

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.600 - 0.041 < p < 0.600 + 0.041

0.558 < p < 0.642

B.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.