Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they acted to annoy a bad driver. In the​ poll, n equals 2536 comma and x equals 928 who said that they honked. Use a 99 % confidence level. a) Find the best point estimate of the population proportion p. .404 . 404 ​(Round to three decimal places as​ needed.) ​b) Identify the value of the margin of error E. Eequals nothing ​(Round to four decimal places as​ needed.) ​c) Construct the confidence interval. nothingless than p less than nothing ​(Round to three decimal places as​ needed.) ​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. A. 99​% of sample proportions will fall between the lower bound and the upper bound. 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 interval from the lower bound to the upper bound actually does contain the true value of the population proportion. D. One has 99​% confidence that the sample proportion is equal to the population proportion

Answer 1

a) $\dpi{100} \widehat p$ = 928/2536 = 0.366

b) At 99% confidence interval the critical value is z_0.005 = 2.58

Margin of error(E) = z_0.005 * sqrt($\dpi{100} \widehat p$(1 - $\dpi{100} \widehat p$ )/n)

                        = 2.58 * sqrt(0.366 * (1 - 0.366)/2536)

                        = 0.0247

c) The 99% confidence interval for population proportion is

$\dpi{100} \widehat p$ +/- E

= 0.366 +/- 0.0247

= 0.3413, 0.3907

= 0.341, 0.391

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