Question

A random sample of Penn State World Campus undergraduate and graduate students were contacted and data concerning their gender identities were recorded. In a random sample of 40 undergraduate students, 21 identified as men and 19 identified as women.  In a random sample of 40 graduate students, 17 identified as men and 23 identified as women. [15 points]

A. Is it appropriate to use the normal approximation method here to construct a confidence interval for the difference in population proportions? Show your work.

B. Construct a 95% confidence interval to compare the proportion of undergraduate students who identify as men to the proportion of graduate students who identify as men. If assumptions were met in part A, use the normal approximation method. Do not do any calculations by hand. Use Minitab Express and remember to copy+paste all relevant output and to clearly identify your final answer.

Answer 1

A random sample of Penn State World Campus undergraduate and graduate students were contacted and data concerning their gender identities were recorded. In a random sample of 40 undergraduate students, 21 identified as men and 19 identified as women.  In a random sample of 40 graduate students, 17 identified as men and 23 identified as women. [15 points]

A. Is it appropriate to use the normal approximation method here to construct a confidence interval for the difference in population proportions? Show your work.

For undergraduate students, proportion of men p =21/40 =0.525

np=40*0.525 =21 and n(1-p) = 40*0.475 = 19 both are > 10

For graduate students, proportion of men p =17/40 =0.425

np=40*0.425 =17 and n(1-p) = 40*0.525 = 23 both are > 10

yes, it is appropriate to use the normal approximation method.

B. Construct a 95% confidence interval to compare the proportion of undergraduate students who identify as men to the proportion of graduate students who identify as men. If assumptions were met in part A, use the normal approximation method. Do not do any calculations by hand. Use Minitab Express and remember to copy+paste all relevant output and to clearly identify your final answer.

For undergraduate students, proportion of men p =21/40 =0.525

Test and CI for One Proportion

Method

p: event proportion

Normal approximation method is used for this analysis.

Descriptive Statistics

N	Event	Sample p	95% CI for p
40	21	0.525000	(0.370245, 0.679755)

95% CI for proportion: ( 0.3702, 0.6798)