Question

In a survey of 3470 adults aged 57 through 85​ years, it was found that 82.3​% of them used at least one prescription medication. Complete parts​ (a) through​ (c) below. a. How many of the 3470 subjects used at least one prescription​ medication? nothing ​(Round to the nearest integer as​ needed.) 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 thanpless than nothing​% ​(Round to one decimal place as​ needed.) c. 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 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). B. The results tell us nothing about the proportion of college students who use at least one prescription medication. C. 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). D. 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).

Answer 1

Solution:

Sample size = n = 3470

Sample proportion = = probability of adults aged 57 through 85​ years used at least one prescription medication = 0.823

Part a. How many of the 3470 subjects used at least one prescription​ medication?

Number of subjects used at least one prescription​ medication = 3470 x 0.823

Number of subjects used at least one prescription​ medication = 2855.81

Number of subjects used at least one prescription​ medication = 2856

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

Formula:

where

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

Thus

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

Since the study is about adults aged 57 through 85​ years who used at least one prescription medication , confidence interval should say about adults aged 57 through 85​ years , not about the college students.

Thus correct option is:

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