anonymous
  • anonymous
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.
Mathematics
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katieb
  • katieb
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anonymous
  • anonymous
@jim_thompson5910 please help!!
jim_thompson5910
  • jim_thompson5910
show me what you have so far
anonymous
  • anonymous
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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anonymous
  • anonymous
*since every participant has to take BOTH tests
jim_thompson5910
  • jim_thompson5910
hmm I'm thinking that everyone has to take both tests since it says `researchers administer both tests to 22 Mexican-Americans`
anonymous
  • anonymous
yes they do
jim_thompson5910
  • jim_thompson5910
Oh I see. You're saying the group of 11 takes the ARSMA first, nvm
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
so yeah that sounds like a good idea to split up the groups
anonymous
  • anonymous
okay, i need help with parts B and C
jim_thompson5910
  • jim_thompson5910
what are the two hypothesis?
anonymous
  • anonymous
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
jim_thompson5910
  • jim_thompson5910
yeah or you can say Ho: mu1 = mu2 Ha: mu1 =/= mu2
jim_thompson5910
  • jim_thompson5910
mu1 = mu2 is the same as mu1 - mu2 = 0
anonymous
  • anonymous
okay! gotcha!
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
ohh okay i see what youre saying
jim_thompson5910
  • jim_thompson5910
strange how alpha isn't given. I'm going to assume it's 0.05
anonymous
  • anonymous
okay! sounds good! okay so this is what i would put in my calc? u0: ? xbar: 0.2519 Sx:0.2767 n:22
jim_thompson5910
  • jim_thompson5910
you went to a t-test right?
anonymous
  • anonymous
yes
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
basically the null hypothesis is that the difference is 0
jim_thompson5910
  • jim_thompson5910
so that is why mu0 is 0
anonymous
  • anonymous
wait in the calculator what would we put in for u0?
jim_thompson5910
  • jim_thompson5910
xbar = 0.2519 s = 0.2767 n = 22
jim_thompson5910
  • jim_thompson5910
0 for mu0
anonymous
  • anonymous
oh okay
anonymous
  • anonymous
im getting t=4.270024322 p=3.4065864E-4
jim_thompson5910
  • jim_thompson5910
3.4065864E-4 is the same as saying 3.4065864 * 10^(-4) = 0.00034065864
jim_thompson5910
  • jim_thompson5910
this p value is very small
jim_thompson5910
  • jim_thompson5910
what does a very small p value tell us?
anonymous
  • anonymous
that we reject the Ho
anonymous
  • anonymous
so there is sufficient evidence to suggest that population mean scores for the two tests were not the same
jim_thompson5910
  • jim_thompson5910
correct on both
anonymous
  • anonymous
is that it for b?
jim_thompson5910
  • jim_thompson5910
yeah
jim_thompson5910
  • jim_thompson5910
that wraps up the hypothesis test
anonymous
  • anonymous
okay what about for C
jim_thompson5910
  • jim_thompson5910
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
jim_thompson5910
  • jim_thompson5910
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
anonymous
  • anonymous
i am getting (.12922, .37458)
jim_thompson5910
  • jim_thompson5910
for me, the data values typed in from the T-test should pop up for the T interval too
jim_thompson5910
  • jim_thompson5910
me too
anonymous
  • anonymous
yes my calc did the same
jim_thompson5910
  • jim_thompson5910
Question: is 0 in that interval?
anonymous
  • anonymous
okay thank you so much! youre the best :)
anonymous
  • anonymous
no
jim_thompson5910
  • jim_thompson5910
so that's more evidence to reject the null. If 0 were in that interval, then the difference could be 0
anonymous
  • anonymous
okay thank you again!!
jim_thompson5910
  • jim_thompson5910
np

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