stat help please

Question

Born between 1980 and 1990, Generation Next is engaged with technology, and the vast ma-

jority is dependent upon it. Suppose that in a survey of 500 female and 500 male students in

Generation Next, 345 of the females and 365 of the males reported that they decided to attend

university in order to make more money.

a) Construct a 98% condence interval for the dierence in the true proportions of female

and male students who decided to attend university in order to make more money. (6 marks)

b) What does it mean to say that you are 98% condent ? (2 marks)

c) Based on the condence interval in part a), can you conclude that there is a dierence in

the proportions of female and male students who decided to attend university in order to make

more money? (2 marks)

Answer 1

The confidence interval for % male - % female -.0267, is [(365/500 - 345/500) - z_.01 *√(365/500*(500-365)/500)/500 + (345/500*(500-345)/500)/500), (365/500 - 345/500) + z_.01 *√(365/500*(500-365)/500)/500 + (345/500*(500-345)/500)/500)] =

[.04 - 2.32634787404084 * 0.0286705423736629, .04 - 2.32634787404084 * 0.0286705423736629] =

[-.0267, .1067]

A 98% confidence interval means that, if we repeat this sampling process, then 98% of the time, the true difference will be in the confidence interval.

0 is in the CI, so we cannot conclude that there is a difference.