In: Statistics and Probability
In a study of cell phone use and brain hemispheric dominance, an internet survey was emailed to 2601 subjects randomly selected from an online group involved with ears. 975 surveys were returned. Construct a 90% confidence interval for the proportion of returned surveys. a) What is the best point estimate of the population P c) Construct the confidence level b) Identify the value of the margin of error E. c) Construct the confidence level.
Solution:
Given:
n = 2601
x = 975
thus
Construct a 90% confidence interval for the proportion of returned surveys.
Part a) What is the best point estimate of the population P
the best point estimate of the population P is sample proportion
that is:
Part b) Identify the value of the margin of error E.
Zc is z critical value for c = 90% confidence level.
Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500
Look in z table for Area = 0.9500 or its closest area and find corresponding z value.
Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500
Thus we look for both area and find both z values
Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65
Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645
Thus Zc = 1.645
thus
Part c) Construct the confidence level.