Question

Use the sample data and confidence level given below to complete parts (a) through (d).

In a study of cell phone use and brain hemispheric dominance, an Internet survey was e-mailed to 2480 subjects randomly selected from an online group involved with ears. 1030 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys.

**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.**

(Round to three decimal places as needed.)

**c) Construct the confidence interval.**

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

A.There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

B.One has 90% confidence that the sample proportion is equal to the population proportion.

C.One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

D. 90 % of sample proportions will fall between the lower bound and the upper bound.

Answer #1

a)

sample proportion, = 0.415

b)

sample size, n = 2480

Standard error, SE = sqrt(pcap * (1 - pcap)/n)

SE = sqrt(0.415 * (1 - 0.415)/2480) = 0.0099

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE

ME = 1.64 * 0.0099

ME = 0.016

c)

CI = (pcap - z*SE, pcap + z*SE)

CI = (0.415 - 1.64 * 0.0099 , 0.415 + 1.64 * 0.0099)

CI = (0.399 , 0.431)

d)

C.One has 90% 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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