You are more interested in comparing the proportions of male and female students

Question

You are more interested in comparing the proportions of male and female students who would buy food containing marijuana. You conduct a survey of randomly selected students and record your data in the file “support.mtw”. The responses of the male students are in the column “support_m” and the responses of the female students are in the column “support_f”.

Data:

support M support F

(a) For the male student and female student populations separately, use Minitab to find 95% confidence intervals for the proportion who would buy food containing marijuana.

(b) Using the sample proportions from Minitab, calculate the standard errors of the two sampling distributions, respectively. Finally calculate manually the same 95% confidence intervals as in part (a).

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Explanation / Answer

Answer:

(a) For the male student and female student populations separately, use Minitab to find 95% confidence intervals for the proportion who would buy food containing marijuana.

Test and CI for One Proportion: support M

Method

Event: support M = yes

p: proportion where support M = yes

Normal approximation method is used for this analysis.

Descriptive Statistics

N

Event

Sample p

95% CI for p

295

194

0.657627

(0.603480, 0.711774)

Test and CI for One Proportion: support F

Method

Event: support F = yes

p: proportion where support F = yes

Normal approximation method is used for this analysis.

Descriptive Statistics

N

Event

Sample p

95% CI for p

297

177

0.595960

(0.540152, 0.651767)

(b) Using the sample proportions from Minitab, calculate the standard errors of the two sampling distributions, respectively. Finally calculate manually the same 95% confidence intervals as in part (a).

Z value for 95% level = 1.96

For male

p=194/295=0.657627

Standard error = sqrt(0.657627*(1-0.657627)/295) =0.027627

95% lower confidence interval = 0.657627-1.96*0.027627 =0.603478

95% upper confidence interval = 0.657627+1.96*0.027627 =0.711776

For female

p=177/297 =0.595960

Standard error = sqrt(0.595960*(1-0.595960)/297) =0.028474

95% lower confidence interval = 0.595960-1.96*0.028474=0.540151

95% upper confidence interval = 0.595960+1.96*0.028474=0.651769

Event: support M = yes

p: proportion where support M = yes

Normal approximation method is used for this analysis.

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