In: Statistics and Probability
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 2562 subjects randomly selected from an online group involved with ears. 1057 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys. 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. Equals nothing (Round to three decimal places as needed.) c) Construct the confidence interval. nothing less 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. 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. One has 90% confidence that the sample proportion is equal to the population proportion. D. There is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
(a)
Question:
Find the best point estimate of the population proportion p.
the best point estimate of the population proportion p. is given by:
= Sample Proportion = 1057/2562 = 0.413
So,
Answer is:
0.413
(b)
Question:
Identify the value of the margin of error E.
From Table, critical values of Z = 1.645
So,
So,
Answer is:
0.016
(c)
Question:
Construct the confidence interval
the confidence interval :
So,
Answer is:
0.397 < p < 0.429
(d)
Question:
Write a statement that correctly interprets the confidence interval. Choose the correct answer below.
Correct option:
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.