Question

Statistics!

Answer 1

A survery was given and here are the results "Number responding less than 1 week" gender - X N
males - 71 411
females - 64 253

a) construct a 95% confidence interval for the difference in the proportions of males and females at this unv. who would respond 'less than one week

b) does there appear to be evidence of a difference in the proportions of men and women at this university who would respond less than 1 week. provide statistical justification

Answer 2

This is how the chart looks

Answer 3

how far did you get with it? were you able to start part a) or b)?

Answer 4

I wasn't sure how to approach doing the confidence interval
I know i'll need the mean, so 71/411 and 64/253 (?)
and im not sure how to do standard deviation.
I guess its the chart thats messing me up

Answer 5

do you know how to calculate the standard error for the proportion?

Answer 6

standard deviation/ square root of sample size

Answer 7

that's for the mean, not proportion

Answer 8

oh sorry! square root of p(1-p)/n p=71/411 = .1727
So (.173)(.827)/411
=.0003481

Answer 9

the square root of that is .01865756..

Answer 10

That's the standard error for the male proportion, call this SE1

Answer 11

for females it would be 64/253 = .2530
so (.253)(.747)/253 = .000747
square root of that = .02733130..

Answer 12

SE2?

Answer 13

good, we'll call that SE2

Answer 14

now to calculate the overall standard error for the difference in proportions between p1 and p2, we square each standard error SE1, SE2 add them up and then take the square root

so

SE = sqrt( (SE1)^2 + (SE2)^2 )

Answer 15

sqrt(.00034810+.000747)
= sqrt (.0010951045)
SE=.0331

Answer 16

good

Answer 17

Any confidence interval is of the form

x +- z*SE

where
x is the point estimate
z is the critical value (we could use a t critical value in its place)
SE is the standard error

Answer 18

so we have SE, which is SE = 0.0331

Answer 19

how do we find z?

Answer 20

Okay So to find the z i opened the t table you had given me in the last problem, so i looked at 95% and not sure where to go from there :(

Answer 21

you're using this table right?

http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg

Answer 22

look in the row that starts with infinity

Answer 23

yup so 1.96

Answer 24

good

Answer 25

the point estimate is the difference between p1 and p2

Answer 26

p1 - p2 = ???

Answer 27

.173-.253=-.08

Answer 28

so you'll have -0.08 +- z*SE

Answer 29

-0.08 is the center of the confidence interval

z*SE is your margin of error

Answer 30

x +- z*SE
-.08+(-1.96)(.0331)
-.144876

Answer 31

+- means plus or minus

Answer 32

oh sorry

Answer 33

so there's going to be two results

the lower limit and the upper limit

Answer 34

lower limit = -0.08 - z*SE

upper limit = -0.08 + z*SE

Answer 35

-.08-.064876 =-.144876
-.08+.064876=-.015124

Answer 36

let me confirm

Answer 37

looks correct to me, nice job

Answer 38

yay!! so thats the 95% confidence interval? right
and for part b could i just right yes there is evidenceof difference in proportion becauseof the difference in standard error

Answer 39

I think you have to do a 2 proportion z test for that part

Answer 40

ugh
so i use z= p1 - p2 / sqrt p(1-p) sqrt (1/n1+ 1/n2)

Answer 41

well the good news is that we have the standard error SE

Answer 42

that was done in part A

Answer 43

the test statistic z is

z = (p1 - p2)/SE

Answer 44

oh wait, does it say anything about pooled samples?

Answer 45

if so, then yeah you have to use

sqrt(p(1-p)(1/n1+ 1/n2))

Answer 46

where

p = (p1*n1 + p2*n2)/(n1+n2)

Answer 47

nope! it just says what i wrote above and the begining blurb says "each person in a random sample of female students and random sample of male students at a particular univeristy was asked, how long ago did u last skip?" the table below shows sample sizes and the numbers who responded less than 1 week ago

Answer 48

so nothing about pooled

Answer 49

ok, well according to this page

http://www.statisticslectures.com/topics/ztestproportions/

Answer 50

we use the formula you posted

Answer 51

so we'll have to go with that

Answer 52

yeah thats the page i read on actually

Answer 53

sooo here we go.
.173-.253
_____________
sqrt.20 (.80) * sqrt 1/411 + 1/253


-.08
_______
(.4)*.079910

-.08
____
.0319641278

=
-2.50280

Answer 54

I'm getting -2.49417125130672, but I'm using up to 10 decimal digits

Answer 55

so it's pretty close

Answer 56

once you have your test statistic, find the area to the left of it and then double that result (this is a two tailed test)

Answer 57

can i use this http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf

Answer 58

you could, but you'd have to work backwards

better to use this

http://www.math.upenn.edu/~chhays/zscoretable.pdf

Answer 59

0.0049 ?

Answer 60

if you're using z = -2.50, the area would be 0.0062

Answer 61

either way, you'll be smaller than 5% (the default significance level)

Answer 62

the p value is even smaller than 1%

Answer 63

we should have set up the hypothesis first, but

Ho: p1 = p2
Ha: p1 =/= p2

the p value is smaller than alpha, so we reject the null and go with p1 =/= p2

that means the proportions are statistically different

Answer 64

oh wait, I forgot to double the area, my bad

Answer 65

0.0062*2 = 0.0124

so you reject at alpha = 0.05

Answer 66

but if alpha = 0.01, then you'd fail to reject

Answer 67

do you just assume alpha .05? since it wasn't stated?

Answer 68

yeah when it's not stated, it's assumed alpha = 0.05 (pretty much every stats textbook, teacher I've seen go to this default)

Answer 69

also, alpha = 1 - (Confidence Level)

so alpha = 1 - 95% = 0.05

Answer 70

so we have evidence of a difference in proportion of men and woman

Answer 71

thank you SOO much!!!!!! SO much!! Wishing you were my proffesor! haha thank you again!!

Answer 72

Yes we have evidence of a difference in proportion of men and woman. I'm glad to be of help