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=1037 and x=509 who said "yes." Use a 99% confidence level.

Click the icon to view a table of z scores.

**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 <p<

(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 9999% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

B.

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

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.

D.

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

Answer #1

Given that, n = 1037 and x = 509

a) sample proportion is,

h

Te best point estimate of the population proportion p is
**0.491**

b) A 99% confidence level has significance level of 0.01 and critical value is,

Margin of error (E) is,

=> E = **0.040**

c) 99% confidence interval for p is,

0.491 - 0.040 < p < 0.491 + 0.040

**0.451 < p < 0.531**

d) Interpretation is,

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.

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