Question

In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2662

subjects randomly selected from an online group involved with ears. 1018 surveys were returned. Construct a

99% 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.

​(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 99% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

B.There is a 99​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

C.One has 99​% confidence that the sample proportion is equal to the population proportion.

D.99​% of sample proportions will fall between the lower bound and the upper bound.

Answer 1

a)

Required estimate =

b)

We know that 99% CI for true proportion is given by:

So, Margin of error =

c)

We know that 99% CI for true proportion is given by:

d)

Interpretation - We have 99% confidence that the interval contains the true value of the population proportion.

Hence option A.