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

2631

subjects randomly selected from an online group involved with ears.

957

surveys were returned. Construct a

90

​%

confidence interval for the proportion of returned surveys.

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Click the icon to view a table of z scores.

​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.

nothing

less than p less thannothing

​(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

90

​%

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

B.

90

​%

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

C.

There is a

90

​%

chance that the true value of the population proportion will fall between the lower bound and the upper bound.

D.

One has

90

​%

confidence that the sample proportion is equal to the population proportion.

Answer 1

Solution(a)
Given in the question
Number of sample(n) = 2631
Number of favourable cases(x) = 957
Sample proportion p^ = x/n = 957/2631 = 0.3637 or 0.364
So best point estimate of population proportion = Sample proportion = 0.364
Solution(b)
Confidence level = 0.90
level of significance or = 1 - Confidence level = 1 - 0.9 = 0.1
/2 = 0.1/2 = 0.05
From Z table we found Zalpha/2 = 1.645
Margin of error E can be calculated as
Margin of error E = Zalpha/2 * sqrt(p^ * (1-p^)/n) = 1.645*sqrt(0.364*(1-0.364)/2631) = 1.645*0.009379 = 0.015
Solution(c)
90% confidence interval can be calculated as
Point estimate +/- Margin of error
0.364 +/- 0.015
So a 90% confidence interval is (0.349<p<0.379)
Solution(d)
Its correct answer is A i.e. 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.