3. A researcher took a simple random sample of four high schools from region wit

Question

3. A researcher took a simple random sample of four high schools from region with 29 high schools for a study on the prevalence of smoking among female high school students in the region. The results were as follows. Number of Number of female Number of female Number of studentsstudents in school students interviewedsmokers School 1471 890 1021 1587 792 447 511 800 10 25 15 20 40 4 27 (a) Estimate the percentage of female high school students in the region who smoke, along with a 95% confidence interval (b) Estimate the total number of female high school students in the region who smoke, along with a 95% confidence interval

Explanation / Answer

a) Total females interviewed = 100

Total smokers = 46

Normal approximation to the binomial calculation:

Standard error of the mean = SEM = x(N-x)/N3 = 0.050

= (1-CL)/2 = 0.025

Standard normal deviate for = Z = 1.960

Proportion of positive results = P = x/N = 0.460

Lower bound = P - (Z*SEM) = 0.362

Upper bound = P + (Z*SEM) = 0.558

CI at 95% = 36.2% and 55.8%

b)

Total number would be a multiplied by the following factor

29(number of schools)* 25.5(total girls in a school) *46*0.362 to 29*25.5*46*0.558

12314 to 18981

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