Question

In a survey of 619 males ages 18-64, 395 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 ( __ _, ___ ). (Round to three decimal places as needed.)

The 95% confidence interval for the population proportion p is (___ , ___ ). (Round to three decimal places as needed.)

Interpret your results of both confidence intervals. Select answer

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 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.

C. 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. Which interval is wider?

Answer 1

The statistical software output for this problem is:

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

90% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	395	619	0.63812601	0.019314638	0.60635626	0.66989576

95% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	395	619	0.63812601	0.019314638	0.60027001	0.67598201

Hence,

90% confidence interval: (0.606, 0.670)

95% confidence interval: (0.600, 0.676)

Interpretation: Option B is correct.

95% confidence interval is wider.