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 2605 subjects randomly selected from an online group involved with ears. 948 surveys were returned. Construct a 95​% confidence interval for the proportion of returned surveys.

​a) Find the best point estimate of the population proportion p.

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

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

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

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

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

D.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.

Answer 1

n = number of subjects randomly selected = 2605

x = number of subjects returned surveys = 948

Confidence level = c = 0.95

a)

Sample proportion:

(Round to 4 decimal)

The best point estimate of the population proportion p is 0.3639

b)

Margin of error (E) :

where zc is z critical value for (1+c)/2 = (1+0.95)/2 = 0.975

zc = 1.96 (From statistical table of z values)

E = 0.018 (Round to 3 decimal)

Margin of error = E = 0.018

c)

95% confidence interval is

(Round to 3 decimal)

95% confidence interval is (0.345, 0.382)

d)

Interpretation:

D.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.