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.

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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.

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@jim_thompson5910 please help!!
show me what you have so far
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.

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*since every participant has to take BOTH tests
hmm I'm thinking that everyone has to take both tests since it says `researchers administer both tests to 22 Mexican-Americans`
yes they do
Oh I see. You're saying the group of 11 takes the ARSMA first, nvm
yes
so yeah that sounds like a good idea to split up the groups
okay, i need help with parts B and C
what are the two hypothesis?
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
yeah or you can say Ho: mu1 = mu2 Ha: mu1 =/= mu2
mu1 = mu2 is the same as mu1 - mu2 = 0
okay! gotcha!
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
ohh okay i see what youre saying
strange how alpha isn't given. I'm going to assume it's 0.05
okay! sounds good! okay so this is what i would put in my calc? u0: ? xbar: 0.2519 Sx:0.2767 n:22
you went to a t-test right?
yes
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
basically the null hypothesis is that the difference is 0
so that is why mu0 is 0
wait in the calculator what would we put in for u0?
xbar = 0.2519 s = 0.2767 n = 22
0 for mu0
oh okay
im getting t=4.270024322 p=3.4065864E-4
3.4065864E-4 is the same as saying 3.4065864 * 10^(-4) = 0.00034065864
this p value is very small
what does a very small p value tell us?
that we reject the Ho
so there is sufficient evidence to suggest that population mean scores for the two tests were not the same
correct on both
is that it for b?
yeah
that wraps up the hypothesis test
okay what about for C
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
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
i am getting (.12922, .37458)
for me, the data values typed in from the T-test should pop up for the T interval too
me too
yes my calc did the same
Question: is 0 in that interval?
okay thank you so much! youre the best :)
no
so that's more evidence to reject the null. If 0 were in that interval, then the difference could be 0
okay thank you again!!
np

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