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9.73 Statistics on Large Sample Tests of Hypotheses?

  1. Oct 13, 2007 #1
    1. The problem statement, all variables and given/known data
    a. Do the data provide sufficient evidence to indicate that the average verbal score for all California students in the class of 2003 is different from the national average? Test using alpha = .05.
    b. Do the data provide sufficient evidence to indicate that the average math score for all California students in the class of 2003 is different from the national average? Test using alpha = .05.
    c. Could you use this data to determine if there is a difference between the average math and verbal scores for all California
    students in the class of 2003? Explain your answer.

    2. Relevant equations
    Relevant DATA:
    n = 100 (California students sampled)
    national average scores for verbal = 507
    sample California average for verbal = 499
    standard dev California for verbal = 98

    Relevant EQUATION:
    z = [sample California average - mean National]
    [standard dev Californial for verbal/sqrt(n)]

    3. The attempt at a solution
    z = [499 - 507]/[98(sqrt(100))]
    = -8/9.8
    = - 0.816

    This answer for part a. is wrong.

    Answers at the back of the book:
    a. yes; z = -3.33 b. no; z = 1 c. no

    I am stuck at part a. My wrong answer is z = -0.816. Please show me how step-by-step to derive at the correct answer. Thank you very much.
     
  2. jcsd
  3. Oct 13, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    I'm confused. You say "My wrong answer is z = -0.816" but none of these questions asks for a value of z! What have you done to answer a?

    In any case, I will point out that [itex]98\sqrt{100}= 980[/itex], not 9.8. The correct z-score is much less than -0.816. (That's assuming that your figure of 100 for the standard deviation is correct. It seems awfully high for average scores around 500. It would pretty much mean that the test is meaningless!)
     
    Last edited: Oct 13, 2007
  4. Oct 13, 2007 #3
    :yuck: I forgot the slash between 98 and sqrt(100)!!!. It was my typo. Sorry.
    Still I get the same answer of z = -0.816 instead of -3.33. I am only concerned about getting the z value because how can I answer yes or no, without knowing it.
    Also, it is asking for us to test using alpha = .05. Z-test is the only test that seems to apply here since we were are comparing a sample (California) from a population (National).
    I also forgot to write the problem statement. I didn't notice it was omitted. See above in red.
     
    Last edited: Oct 13, 2007
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