In a survey of 606 males ages 18-64, 396 say they have gone to the dentist in th

Question

In a survey of 606 males ages 18-64, 396 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 96% 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 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? The 90% confidence interval The 96% confidence interval

Explanation / Answer

The pic is not clear, so I am assuming the values are 606 and 396.

Sample proportion:

p' = 396/606 = 0.653

Standard error SE = (p'*(1-p')/n)0.5 = (0.653*0.347/606)0.5 = 0.019

For 90% CI, the critical z-score is: zc = 1.64

So, 90% CI is:

p'-(zc*SE) < p < p'+(zc*SE)

Putting values:

0.653-(1.64*0.019) < p < 0.653+(1.64*0.019)

0.622 < p < 0.684

Width of 90% interval = 0.684-0.622 = 0.062

For 95% CI, the critical z-score is: zc = 1.96

So, 95% CI is:

p'-(zc*SE) < p < p'+(zc*SE)

Putting values:

0.653-(1.96*0.019) < p < 0.653+(1.96*0.019)

0.615 < p < 0.690

Width of 95% interval = 0.690-0.615 = 0.075

Correct option for next part is (B): With the given confidence it can be said that the population proportion of ... is between the end points of the interval

The wider interval is of 95%

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