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.