A CNN Poll was conducted by Gallup, from Feb. 8 to Feb. 15, 2009. 1,501 adults w

ID: 3174116 • Letter: A

Question

A CNN Poll was conducted by Gallup, from Feb. 8 to Feb. 15, 2009. 1,501 adults were interviewed by phone. 1186 of them responded “Economy is getting worse” to the question “Has President Obama made any change in the way Americans view the U.S. Economy?”

(a) Identify population and parameter.

(b) Find the sample proportion of people who think that the economy is getting worse. Also find the margin of error.

(c) Find a 95% confidence interval for the population proportion of people who think that the economy is getting worse. Interpret the interval.

(d) What does margin of error measure?

Explanation / Answer

Result:

(a) Identify population and parameter.

population : All adults who are have phone

parameter: proportion of all adults with response Economy is getting worse.

(b) Find the sample proportion of people who think that the economy is getting worse. Also find the margin of error.

sample proportion p=1186/1501 = 0.7901

standard error = sqrt(0.7901*(1-0.7901)/1501)

=0.0105

95% margin of error= 1.96*0.0105 =0.0206

(c) Find a 95% confidence interval for the population proportion of people who think that the economy is getting worse. Interpret the interval.

95% CI = (0.7695, 0.8107)

(d) What does margin of error measure?

The margin of error is a measure of the precision of a sample estimate of the population value. It uses probability to demonstrate the precision of a sample estimate by providing a range of values in which a sample value would be expected to fall.

Confidence Interval Estimate for the Proportion

Data

Sample Size

1501

Number of Successes

1186

Confidence Level

95%

Intermediate Calculations

Sample Proportion

0.7901

Z Value

1.9600

Standard Error of the Proportion

0.0105

Interval Half Width

0.0206

Confidence Interval

Interval Lower Limit

0.7695

Interval Upper Limit

0.8107