You are more interested in comparing the proportions of male and female students
ID: 3040633 • Letter: Y
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”.
(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).
support_m support_f
yes yes
no no
no yes
yes no
yes no
yes yes
yes no
yes yes
no no
yes yes
yes yes
yes no
no no
yes no
no yes
yes no
yes no
no no
yes no
no yes
yes yes
yes yes
yes no
no yes
yes yes
no yes
yes yes
yes yes
yes yes
yes yes
yes yes
yes no
yes no
no yes
yes no
yes no
no no
yes no
yes no
yes yes
no no
no no
no no
no yes
yes yes
yes yes
yes no
no yes
yes no
no yes
no no
yes yes
no yes
no yes
no yes
yes yes
yes no
yes yes
no yes
yes yes
no yes
no no
yes yes
no yes
yes yes
yes no
no yes
no no
yes yes
no yes
yes no
no no
yes yes
yes yes
no no
yes yes
yes no
yes yes
yes no
yes yes
yes yes
yes yes
yes no
yes yes
yes yes
yes no
yes no
yes yes
no no
yes yes
no no
yes yes
yes yes
no yes
yes yes
no yes
yes yes
yes yes
yes yes
no no
no no
yes yes
yes yes
no no
yes no
no yes
yes yes
no no
yes yes
no no
yes no
no no
yes no
yes yes
no yes
no no
yes yes
no no
yes yes
yes no
yes no
yes no
no yes
no yes
yes no
no yes
yes no
yes yes
no yes
yes yes
no no
yes yes
yes yes
yes no
no yes
yes no
no yes
yes yes
no no
no yes
yes yes
yes yes
yes no
yes no
yes yes
yes yes
yes no
yes no
yes no
yes yes
yes yes
no no
no yes
yes no
no no
yes yes
yes yes
yes yes
no yes
no yes
no yes
yes yes
yes no
yes no
yes no
no yes
no no
no yes
yes no
yes no
yes yes
no no
yes yes
yes no
yes no
yes yes
no yes
no no
yes yes
yes no
no yes
yes yes
no no
no yes
yes yes
yes yes
yes yes
yes yes
yes yes
yes yes
no no
no no
yes yes
yes yes
yes yes
no no
yes yes
yes yes
no yes
yes yes
yes yes
yes no
yes yes
yes yes
no no
yes no
no yes
no yes
yes yes
yes yes
yes yes
yes yes
yes yes
yes yes
yes no
yes no
yes no
yes yes
no no
yes no
yes yes
yes no
yes no
no no
yes no
yes yes
yes yes
yes yes
yes yes
yes yes
no yes
no yes
yes yes
yes yes
yes no
yes no
yes no
no yes
yes yes
yes no
no yes
yes yes
yes yes
yes yes
yes yes
yes no
yes no
no no
no no
yes yes
yes yes
yes yes
no yes
no no
no no
no no
yes no
no no
yes yes
no yes
yes no
no no
yes yes
yes no
yes yes
yes yes
yes yes
no no
yes no
no yes
yes yes
no no
yes no
yes no
yes yes
yes yes
no yes
yes yes
yes yes
no no
yes yes
no yes
yes yes
yes no
no no
no yes
yes yes
yes yes
yes yes
no yes
yes yes
no yes
yes yes
no yes
yes yes
yes
no
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.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.