Question

Q4. In a survey of

3272

adults aged 57 through 85​ years, it was found that

81.1​%

of them used at least one prescription medication.

b. Construct a​ 90% confidence interval estimate of the percentage of adults aged 57 through 85 years who use at least one prescription medication.

nothing​%less than<pless than<nothing​%

​(Round to one decimal place as​ needed.)

What do the results tell us about the proportion of college students who use at least one prescription​ medication?

A.The results tell us​ that, with​ 90% confidence, the probability that a college student uses at least one prescription medication is in the interval found in part​ (b).

B.The results tell us that there is a​ 90% probability that the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b).

C.The results tell us​ that, with​ 90% confidence, the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b).

D.The results tell us nothing about the proportion of college students who use at least one prescription medication.

Answer 1

Level of Significance,   α =    0.10          
Sample Size,   n =    3272          
                  
Sample Proportion ,    p̂ = 0.811          
z -value =   Zα/2 =    1.645 [excel formula =NORMSINV(α/2)]      
                  
Standard Error ,    SE = √[p̂(1-p̂)/n] =    0.0068          
margin of error , E = Z*SE =    1.645   *   0.0068   =   0.0113
                  
90%   Confidence Interval is              
Interval Lower Limit = p̂ - E =    0.811   -   0.0113   =   0.7997
Interval Upper Limit = p̂ + E =   0.811   +   0.0113   =   0.8223
                  
90%   confidence interval is (   8.0% < p < 8.2 % )

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C.The results tell us​ that, with​ 90% confidence, the true proportion of college students who use at least one prescription medication is in the interval found in part​ (b).