## anonymous one year ago 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.

1. anonymous

2. jim_thompson5910

show me what you have so far

3. 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.

4. anonymous

*since every participant has to take BOTH tests

5. jim_thompson5910

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

6. anonymous

yes they do

7. jim_thompson5910

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

8. anonymous

yes

9. jim_thompson5910

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

10. anonymous

okay, i need help with parts B and C

11. jim_thompson5910

what are the two hypothesis?

12. 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

13. jim_thompson5910

yeah or you can say Ho: mu1 = mu2 Ha: mu1 =/= mu2

14. jim_thompson5910

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

15. anonymous

okay! gotcha!

16. 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

17. anonymous

ohh okay i see what youre saying

18. jim_thompson5910

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

19. anonymous

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

20. jim_thompson5910

you went to a t-test right?

21. anonymous

yes

22. 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

23. jim_thompson5910

basically the null hypothesis is that the difference is 0

24. jim_thompson5910

so that is why mu0 is 0

25. anonymous

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

26. jim_thompson5910

xbar = 0.2519 s = 0.2767 n = 22

27. jim_thompson5910

0 for mu0

28. anonymous

oh okay

29. anonymous

im getting t=4.270024322 p=3.4065864E-4

30. jim_thompson5910

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

31. jim_thompson5910

this p value is very small

32. jim_thompson5910

what does a very small p value tell us?

33. anonymous

that we reject the Ho

34. anonymous

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

35. jim_thompson5910

correct on both

36. anonymous

is that it for b?

37. jim_thompson5910

yeah

38. jim_thompson5910

that wraps up the hypothesis test

39. anonymous

40. 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

41. 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

42. anonymous

i am getting (.12922, .37458)

43. jim_thompson5910

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

44. jim_thompson5910

me too

45. anonymous

yes my calc did the same

46. jim_thompson5910

Question: is 0 in that interval?

47. anonymous

okay thank you so much! youre the best :)

48. anonymous

no

49. jim_thompson5910

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

50. anonymous

okay thank you again!!

51. jim_thompson5910

np

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