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 = 2592, and x =1096 who said that they honked. Use a 99 % confidence level.

​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.

E=____ ​(Round to four 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 99%confidence that the sample proportion is equal to the population proportion.

B.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

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

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

Answer 1

Solution :

Given that,

n = 2592

x = 1096

Point estimate = sample proportion = = x / n = 1096 / 2590 = 0.423

1 - = 0.577

Z_/2 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.423 * 0.577) / 2592)

= 0.025

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.423 - 0.025 < p < 0.425 + 0.025

0.398 < p < 0.448

B.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