In a survey of 603 males ages 18-64, 391 say they have gone to the dentist in th

Question

In a survey of 603 males ages 18-64, 391 say they have gone to the dentist in the past year. Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. The 90% confidence interval for the population proportion p is (, ). The 95% confidence interval for the population proportion p is (, ). Interpret your results of both confidence intervals. A. With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is not between the endpoints of the given confidence interval. B. With the given confidence, it can be said that the sample proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval. C. With the given confidence, it can be said that the population proportion of males ages 18-64 who say they have gone to the dentist in the past year is between the endpoints of the given confidence interval. Which interval is wider? The 90% confidence interval The 95% confidence interval

Explanation / Answer

The statistical software output for 90% and 95% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:

95% confidence interval results:

Hence,

90% confidence interval:

(0.616, 0.680)

95% confidence interval:

(0.610, 0.687)

Interpretation of confidence interval: Option C is correct.

The 95% confidence interval is wider.

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 391 603 0.64842454 0.019443764 0.6164424 0.68040669

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