Question

Question Help - 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 2376 subjects randomly selected from an online group involved with ears. 955 surveys were returned. Construct a 95% confidence interval for the proportion of returned surveys Click the icon to view a table of z scores 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. O A. 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. B. 95% of sample proportions will fall between the lower bound and the upper bound C. There is a 95% chance that the true value of the population proportion will fall between the lower bound and the upper bound D. One has 95% confidence that the sample proportion is equal to the population proportion Click to select your answerls)

Answer 1

Given that, n = 2376 and x = 955

confidence level = 95%

A 95% confidence level has significance level $(\alpha)$ = 0.05 and has critical value is, $Z_{\alpha/2}= 1.96$

a) The best point estimate of the population proportion is,

$\hat p = \frac { x }{n }= \frac { 955}{2376}= 0.402$

b) Margin of error ( E ) is,

$E = Z_{\alpha/2} * \sqrt {\frac { \hat p *(1-\hat p)}{n}} = 1.96 * \sqrt {\frac { 0.402 *(1-0.402)}{2376}} = 0.020$

E = 0.020

c) confidence intervsl for p is,

$\hat p - E < p < \hat p &plus; E$

$0.402 - 0.020 < p < 0.402 &plus; 0.020$

$0.382 < p < 0.422$

d) Interpretation of above confidence interval is,

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.