Question

The Acculturation Rating Scale for Mexican Americans (ARSMA) is a test that measures the extent to which Mexican Americans have adopted Anglo/English culture. A similar test, the Bicultural Inventory (BI), attempts to do the same thing. To compare the tests, researchers administer both tests to 22 Mexican-Americans. Both tests have the same range of scores (1.00 to 5.00) and are scaled to have similar means for the groups used to develop them. There was a high correlation between the two scores, giving evidence that both are measuring the same characteristics. The researchers wanted to know whether the population mean scores for the two tests were the same. The differences in scores (ARSMA - BI) for the 22 subjects had x = 0.2519 and s = 0.2767.

(a) Describe briefly how the administration of the two tests to the subjects should be conducted, including randomization.
(b) Carry out a significance test for the hypothesis that the two tests have the same population mean. Give the P-value and state your conclusions.
(c) Give a 95% confidence interval for the difference between the two population mean scores.

Answer 1

@jim_thompson5910 please help!!

Answer 2

show me what you have so far

Answer 3

okay well for a: i know we must try to avoid the two tests influencing each other. but since every participant has to take the test we should split the group in half. 11 will take the ARSMA test first and the other 11 will take the BI first. this can be determined by a random drawing such as numbers out of a hat or certain colored items, etc.

Answer 4

*since every participant has to take BOTH tests

Answer 5

hmm I'm thinking that everyone has to take both tests since it says `researchers administer both tests to 22 Mexican-Americans`

Answer 6

yes they do

Answer 7

Oh I see. You're saying the group of 11 takes the ARSMA first, nvm

Answer 8

yes

Answer 9

so yeah that sounds like a good idea to split up the groups

Answer 10

okay, i need help with parts B and C

Answer 11

what are the two hypothesis?

Answer 12

im not quite sure how to conduct a significance test on the ti 84 calculator given the data provided.

two hypothesis:
Ho: the population mean scores for the two tests were the same
Ha: the population mean scores for the two tests were not the same

Answer 13

yeah or you can say

Ho: mu1 = mu2
Ha: mu1 =/= mu2

Answer 14

mu1 = mu2 is the same as mu1 - mu2 = 0

Answer 15

okay! gotcha!

Answer 16

this seems like a paired t-test because we aren't given the xbar value for the ARSMA group (or the BI group). Instead we're given the xbar value for the difference in the scores

Answer 17

ohh okay i see what youre saying

Answer 18

strange how alpha isn't given. I'm going to assume it's 0.05

Answer 19

okay! sounds good! okay so this is what i would put in my calc?
u0: ?
xbar: 0.2519
Sx:0.2767
n:22

Answer 20

you went to a t-test right?

Answer 21

yes

Answer 22

ok so recall that mu1 - mu2 = 0 is the null

the difference in the means, call it mu_D, is

mu_D = mu1 - mu2 = 0

so, mu_D = 0

Answer 23

basically the null hypothesis is that the difference is 0

Answer 24

so that is why mu0 is 0

Answer 25

wait in the calculator what would we put in for u0?

Answer 26

xbar = 0.2519
s = 0.2767
n = 22

Answer 27

0 for mu0

Answer 28

oh okay

Answer 29

im getting t=4.270024322
p=3.4065864E-4

Answer 30

3.4065864E-4 is the same as saying 3.4065864 * 10^(-4) = 0.00034065864

Answer 31

this p value is very small

Answer 32

what does a very small p value tell us?

Answer 33

that we reject the Ho

Answer 34

so there is sufficient evidence to suggest that population mean scores for the two tests were not the same

Answer 35

correct on both

Answer 36

is that it for b?

Answer 37

yeah

Answer 38

that wraps up the hypothesis test

Answer 39

okay what about for C

Answer 40

the confidence interval (L,U) will use the formulas

L = xbar - t*s/(sqrt(n))
U = xbar + t*s/(sqrt(n))

where t is the critical value

Answer 41

you can use the calculator to go to hit the "STAT" key, then scroll down to #8 (or just hit the "8" key) to get to TInterval

Answer 42

i am getting (.12922, .37458)

Answer 43

for me, the data values typed in from the T-test should pop up for the T interval too

Answer 44

me too

Answer 45

yes my calc did the same

Answer 46

Question: is 0 in that interval?

Answer 47

okay thank you so much! youre the best :)

Answer 48

no

Answer 49

so that's more evidence to reject the null. If 0 were in that interval, then the difference could be 0

Answer 50

okay thank you again!!

Answer 51

np