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 1079 and x equals 513 who said "yes." Use a 95 % confidence level.

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. a) Find the best point estimate of the population proportion p. nothing (Round to three decimal places as needed.)

b) Identify the value of the margin of error E. Eequals nothing (Round to three decimal places as needed.)

c) Construct the confidence interval. nothingless than p less than nothing (Round to three decimal places as needed.)

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

A. 95 % of sample proportions will fall between the lower bound and the upper bound.

B. One has 95 % confidence that the sample proportion is equal to the population proportion

. C. One has 95 % confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion

. D. There is a 95 % chance that the true value of the population proportion will fall between the lower bound and the upper bound.

Answer 1

Solution :

Given that,

n = 1079

x = 513

Point estimate = sample proportion = = x / n = 513 / 1079 = 0.475

1 - = 0.525

Z_/2 = 1.96

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

= 1.96 * (((0.475 * 0.525) / 1079)

= 0.029

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.475 - 0.029 < p < 0.475 + 0.029

0.446 < p < 0.0504

One has 95 % confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion

C)