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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.

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  1. anonymous
    • one year ago
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    @jim_thompson5910 please help!!

  2. jim_thompson5910
    • one year ago
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    show me what you have so far

  3. anonymous
    • one year ago
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    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
    • one year ago
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    *since every participant has to take BOTH tests

  5. jim_thompson5910
    • one year ago
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    hmm I'm thinking that everyone has to take both tests since it says `researchers administer both tests to 22 Mexican-Americans`

  6. anonymous
    • one year ago
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    yes they do

  7. jim_thompson5910
    • one year ago
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    Oh I see. You're saying the group of 11 takes the ARSMA first, nvm

  8. anonymous
    • one year ago
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    yes

  9. jim_thompson5910
    • one year ago
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    so yeah that sounds like a good idea to split up the groups

  10. anonymous
    • one year ago
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    okay, i need help with parts B and C

  11. jim_thompson5910
    • one year ago
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    what are the two hypothesis?

  12. anonymous
    • one year ago
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    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
    • one year ago
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    yeah or you can say Ho: mu1 = mu2 Ha: mu1 =/= mu2

  14. jim_thompson5910
    • one year ago
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    mu1 = mu2 is the same as mu1 - mu2 = 0

  15. anonymous
    • one year ago
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    okay! gotcha!

  16. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    ohh okay i see what youre saying

  18. jim_thompson5910
    • one year ago
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    strange how alpha isn't given. I'm going to assume it's 0.05

  19. anonymous
    • one year ago
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    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
    • one year ago
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    you went to a t-test right?

  21. anonymous
    • one year ago
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    yes

  22. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    basically the null hypothesis is that the difference is 0

  24. jim_thompson5910
    • one year ago
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    so that is why mu0 is 0

  25. anonymous
    • one year ago
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    wait in the calculator what would we put in for u0?

  26. jim_thompson5910
    • one year ago
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    xbar = 0.2519 s = 0.2767 n = 22

  27. jim_thompson5910
    • one year ago
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    0 for mu0

  28. anonymous
    • one year ago
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    oh okay

  29. anonymous
    • one year ago
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    im getting t=4.270024322 p=3.4065864E-4

  30. jim_thompson5910
    • one year ago
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    3.4065864E-4 is the same as saying 3.4065864 * 10^(-4) = 0.00034065864

  31. jim_thompson5910
    • one year ago
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    this p value is very small

  32. jim_thompson5910
    • one year ago
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    what does a very small p value tell us?

  33. anonymous
    • one year ago
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    that we reject the Ho

  34. anonymous
    • one year ago
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    so there is sufficient evidence to suggest that population mean scores for the two tests were not the same

  35. jim_thompson5910
    • one year ago
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    correct on both

  36. anonymous
    • one year ago
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    is that it for b?

  37. jim_thompson5910
    • one year ago
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    yeah

  38. jim_thompson5910
    • one year ago
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    that wraps up the hypothesis test

  39. anonymous
    • one year ago
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    okay what about for C

  40. jim_thompson5910
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    i am getting (.12922, .37458)

  43. jim_thompson5910
    • one year ago
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    for me, the data values typed in from the T-test should pop up for the T interval too

  44. jim_thompson5910
    • one year ago
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    me too

  45. anonymous
    • one year ago
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    yes my calc did the same

  46. jim_thompson5910
    • one year ago
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    Question: is 0 in that interval?

  47. anonymous
    • one year ago
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    okay thank you so much! youre the best :)

  48. anonymous
    • one year ago
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    no

  49. jim_thompson5910
    • one year ago
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    so that's more evidence to reject the null. If 0 were in that interval, then the difference could be 0

  50. anonymous
    • one year ago
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    okay thank you again!!

  51. jim_thompson5910
    • one year ago
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    np

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