Question

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). A research institute poll asked respondents if they felt vulnerable to identity theft. In the​ poll, n equals 1038 and x equals 567 who said​ "yes." Use a 95 % confidence level. LOADING... 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. 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. There is a 95​% chance that the true value of the population proportion will fall between the lower bound and the upper bound. B. 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. C. 95​% of sample proportions 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 answer(s).

Answer 1

Given that, n = 1038 and x = 567

=> Sample proportion = 567/1038 = 0.546

a) The best point estimate of the population proportion p is 0.546

b) A 95% confidence level has significance level of 0.05 and critical value is,

We want to find the margin of error (E),

=> Margin of error = E = 0.030

c) The 95% confidence interval for p is,

0.546 - 0.030 < p < 0.546 + 0.030

0.516 < p < 0.576

d) One has 95​% confidence that the interval from the lower bound = 0.516 to the upper bound = 0.576 actually does contain the true value of the population proportion.