Question

In a survey of 625 males ages​ 18-64, 393 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. Choose the correct answers

A. 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.

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 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.

Which interval is​ wider? Choose the correct answers.

a.The​ 90% confidence interval

b.The​ 95% confidence interval

Answer 1

Proportion of population going to dentist (p) = 393/625=0.6288
Standard Error = t value * (p*(1-p)/n)^0.5
Fpr CI = 90%
t distribution has to be used since standrad deviation not known
alpha = 1- 10%/2 = 95%
Degree of Freedom = 625 -1 = 624
critical value from t table = 1.647
Standard Error (p*(1-p)/n)^0.5 = (0.6288*(1-0.6288)/625)^0.5 = 0.019325
a)The​ 90% confidence interval for the population proportion p is (0.6288 - 1.647*0.019325,0.6288 + 1.647*0.019325) = (0.597,0.661)

alpha = 1- 5%/2 = 97.5%
Degree of Freedom = 625 -1 = 624
critical value from t table = 1.964
The​ 95% confidence interval for the population proportion p is (0.6288 - 1.964*0.019325,0.6288 + 1.964*0.019325) = (0.591,0.667)

Interpret your results of both confidence intervals. Choose the correct answers

Option B is Correct. 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)Option b The​ 95% confidence interval is correct

Please discuss in case of doubt