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StClowers Group Title

An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (a) The required sample size is ____. (Round up to one integer as needed) (b) Is this sample size reasonable?

  • 7 months ago
  • 7 months ago

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  1. mathmale Group Title
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    You'll find a formula for required sample size in the same chapter that discusses confidence intervals. You're given all the info necessary to calculate this minimum sample size: confidence level (90%), standard deviation (17) and acceptable margin of error (5). Please look for this formula.

    • 7 months ago
  2. StClowers Group Title
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    But i have no idea how to calculate this

    • 7 months ago
  3. mathmale Group Title
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    Your formula is basically OK, but you must square the quantity within parentheses. also, you're dividing that (z-score)(sigma) by E.

    • 7 months ago
  4. mathmale Group Title
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    z, as you've written it, is called the "z critical value" and is, I believe, 1.645 for 90% confidence.

    • 7 months ago
  5. mathmale Group Title
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    Please be sure you know how to find that; if you don't, either someone else or I can explain where that comes from. Forgive me, but I need to get off my computer; if by the time I come back on, someonehas not helped you complete this problem already, I certainly will. Thanks, ybarrap.

    • 7 months ago
  6. StClowers Group Title
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    Im so lost in statistics....I have no idea....can you please help me compute this problem?

    • 7 months ago
  7. ybarrap Group Title
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    Use the students t-value: $$ \large{ \bar x\pm\cfrac{t_{(1-c)/2}}{\sqrt n}\\ } $$ Where c = 0.90 so (1-c)/2 = .05 Now let's find \(t_{.05}\), the two-tail student's t at the .05 significance level. Can you find that? Then you want: $$ \cfrac{t_{(1-c)/2}}{\sqrt n}=5 $$ Now you are left with an equation that you can solve for n. Does this help?

    • 7 months ago
  8. StClowers Group Title
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    Ont he calculator you gave me, when i plugged in the numbers...then entered my answer, it was wrong. ugh

    • 7 months ago
  9. ybarrap Group Title
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    I forgot to include the sample variance, s: $$ \large{ \bar x\pm\cfrac{t_{(1-c)/2}s}{\sqrt n}\\ } $$ So then find $$ \cfrac{t_{(1-c)/2}s}{\sqrt n}=5 $$

    • 7 months ago
  10. ybarrap Group Title
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    You need the student's t-value at the .05 significance level. Get that and you should be done. The calculator is just a validation-- you need to know how to look up this value.

    • 7 months ago
  11. StClowers Group Title
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    no clue. I think the answer is 32 but have no idea how to get that

    • 7 months ago
  12. mathmale Group Title
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    I'm back. The formula (you typed earlier in this conversation) for the minimum number of samples is (after a correction or two): \[n=(\frac{ [z critical value][standard deviation] }{ E })^{2}\] Not that this is essentially the same as yours, except that I've indicated division by a horiz. line and have squared the quantity within parentheses.

    • 7 months ago
  13. mathmale Group Title
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    z, the z-critical value corresponding to a 90% confidence interval, is 1.28 (not 1.645, as I typed in earlier). The standard deviation given in the problem statement is 17. E is the "margin of error;" we're hoping that we can estimate the "true mean" to within E, or 5. Putting this all together gives us \[n=(\frac{ (1.28)(17) }{ 5 })^{2}.\]

    • 7 months ago
  14. mathmale Group Title
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    I've calculated this and have obtained as result n = 18.94. This must be rounded UP, to 19, which represents the minimum number of samples you must work with in order not to be further than 5 IQ points of the true mean IQ.

    • 7 months ago
  15. StClowers Group Title
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    is that the answer then? I am so beyond frustrated that I cannot figure this stuff out.

    • 7 months ago
  16. mathmale Group Title
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    First, please read this thru and decide whether or not the process is clear to you. Have you calculated (or looked up) z-critical values before? For a 99% confidence interval, the z-critical value is 2.33; for 95%, it's 1.645, and for 90% (with which you're dealing here), it is 1.28. That's where the 1.28 in the formula for n came from. Please see: http://easycalculation.com/statistics/z-critical-value.php If you type in 90%, this calculator will return 1.28.

    • 7 months ago
  17. mathmale Group Title
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    I'd certainly like for you to feel comfortable and confident in dealing with this sort of problem. Can you think of any questions to ask that might help you come to a clearer understanding of what's happening here? Where did you obtain that "32" figure that you thought was the answer?

    • 7 months ago
  18. StClowers Group Title
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    thats what it said when i typed that into the box where i put the answer. I have cried over trying to figure this out...sorry Im difficult. I have no idea what the answer is or how to get it. I dont even know what to say to answer your question

    • 7 months ago
  19. StClowers Group Title
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    This homeowrk is due now and i dont have a clue.

    • 7 months ago
  20. mathmale Group Title
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    What kind of reference(s) (if any) do you have available to you? Have you been able to locate the formula you typed out for me 'way back? Where did you get it? Except for not being squared, your expression looked OK.

    • 7 months ago
  21. StClowers Group Title
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    thank you for helping. I am really trying but Im not understanding these formulas.

    • 7 months ago
  22. StClowers Group Title
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    my work is out of the mymathlabs and it was a formula given in the example...

    • 7 months ago
  23. StClowers Group Title
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    its all foreign language to me

    • 7 months ago
  24. mathmale Group Title
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    Although I can't stay online for more than a few minutes longer, perhaps I could help you tomorrow or later to understand those formulas. What deadlines are you working with?

    • 7 months ago
  25. StClowers Group Title
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    its due tomorrow but i have 5 more questions. bleh

    • 7 months ago
  26. mathmale Group Title
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    I don't have reason to doubt the accuracy of the problem we've supposedly just completed. I'd type in "19" for the minimum number of samples you'd need. Pick one more of those questions and post it, as quickly as you can.

    • 7 months ago
  27. mathmale Group Title
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    Please post it as an entirely new question. (This assumes, of course, that you want to and have time to do so now.)

    • 7 months ago
  28. StClowers Group Title
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    I will. thank you. they are already posted but noone is answering them - it wont let me post again

    • 7 months ago
  29. StClowers Group Title
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    An IQ test is designed so that the mean is 100 and the standard deviation is 19 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 95% confidence that the sample mean is within 2 IQ points of the true mean. Assume that Ơ = 19 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation. (a) The required sample size is ____. (Round up to one integer as needed) (b) Is this sample size reasonable?

    • 7 months ago
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