Question

1. In a magazine that has 98 pages of adds of the 152 pages total: a. Based on this sample result, construct a 95% confidence interval estimate of the percentage of all popular magazine pages that have advertising. (See section 7-2 of the textbook for examples of such confidence intervals). b. Give a description of what this confidence interval tells you about magazine advertising. c. What would change about your confidence interval if you changed the confidence level to 99%?

Answer 1

Solution:

Given:

n = 152

x = 98

Sample proportion magazine that has pages of adds is:

Part a. Based on this sample result, construct a 95% confidence interval estimate of the percentage of all popular magazine pages that have advertising.

Formula:

where

We need to find z_c value for c=95% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.95) /2 = 1.95 / 2 = 0.9750

Look in z table for Area = 0.9750 or its closest area and find z value.

Area = 0.9750 corresponds to 1.9 and 0.06 , thus z critical value = 1.96

That is : Z_c = 1.96

Thus

Thus

Part b. Give a description of what this confidence interval tells you about magazine advertising

We are 95% confident that true estimate of the percentage of all popular magazine pages that have advertising. is between the limits :

Part c. What would change about your confidence interval if you changed the confidence level to 99%?

As the confidence level increases, Margin of Error increases and hence length of confidence interval is also increases.

Thus 99% confidence interval would be more wider than 95% confidence interval.