Question

In a survey of 2433 adults in a recent year, 1369 say they have made a New Year's resolution.

Construct 90% and 95% confidence intervals for the population proportion. interpret the results and compare the withs of the confidence intervals.

90% (__,__)

95%(__,__)

(Round to three decimal places as needed)

Answer 1

A) Let x= Number of adults who say that they have made a New Year's resolution=1369

sample size = n = 2433

Confidence levele = 0.90

Therefore sample proportion is

90% confidence intervals for the population proportion is

Where

Margin of error =

Zc = Critical value of C = 1.645 ...............( By using Z table)

The 90% confidence intervals for the population proportion is

...............( ANSWER)

The 90% confidence intervals for the population proportion is (0.546,0.579)...........( ANSWER)

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B) Let x= Number of adults who say that they have made a New Year's resolution=1369

sample size = n = 2433

Confidence levele = 0.95

Therefore sample proportion is

95% confidence intervals for the population proportion is

Where

Margin of error =

Zc = Critical value of C = 1.96 ...............( By using Z table)

The 95% confidence intervals for the population proportion is

...............( ANSWER)

The 95% confidence intervals for the population proportion is (0.543,0.582)...........( ANSWER)

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The 90% confidence intervals for the population proportion is (0.546,0.579) and

The 95% confidence intervals for the population proportion is (0.543,0.582)

Width of confidence intervals= Upper limit - Lower limit

For 90% confidence intervals

width of C.I. = 0.579-0.546=0.033 and

For 95% confidence intervals

width of C.I. = 0.582-0.543=0.039

i.e.The width increases as the confidence level increases