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Math Help - Hypothesis testing

  1. #1
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    Unhappy Hypothesis testing

    A recent study stated that if a person smoked, the average of the number of

    cigarettes he or she smoked was 14 per day. To test the claim, a researcher

    selected a random sample of 40 smokers and found that the mean number of

    cigarettes smoked per day was 18. The standard deviation of the sample was 6. At

    0.05(alpha), is the number of cigarettes a person smokes per day actually different

    from 14?

    Here's my work:

    H(0): mean = 14 and H(1): mean =/= 14

    z-test for the mean.

    i used, 1.65 as the line. and used the equation: z = (X-mean)/(st.d / sqrt(n)).

    so i got, (18-14)/(6/sqrt(40)) = 4.22.... which would reject the hypothesis. Am I

    doing this right?
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  2. #2
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    Quote Originally Posted by driver327 View Post
    Am I doing this right?
    I think so, just needs a little refining.



    Quote Originally Posted by driver327 View Post

    i used, 1.65 as the line.
    Why? what value for alpha does this give?

    How will you write your conclusion.
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  3. #3
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    it gave .05 as the alpha. i said it should be rejected because the 4.22 is greater than

    1.65... and therefore, there is not enough evidence to support the claim. I wasn't

    confident because I thought the number was a bit

    high.
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  4. #4
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    The logic is correct, if the calculated value is bigger than the critical value then you reject H_0.

    The question is have you got the correct calculated value? Because you only have the standard deviation of the sample ( s) and not the population ( \sigma) you should employ a t-test.

    I.e Reject H_0 if \displaystyle t_{\text{calc}} = \frac{\bar{X}-\mu_0}{\frac{s}{\sqrt{n}}}>t_{\text{crit}} = t_{\alpha , \text{df}}
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  5. #5
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    i just calculated it, and got the same answer. the only difference was the critical pt. is now 2.0225. If i'm still wrong, then I must be missing something.
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  6. #6
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    Quote Originally Posted by driver327 View Post
    i just calculated it, and got the same answer. the only difference was the critical pt. is now 2.0225. If i'm still wrong, then I must be missing something.

    I have not done the workings myself, but it seems reasonable to me, if you have followed these steps you should be confident in your answer, given there are no silly arithmetic errors.

    Just remember, as the sample size gets very large then t \rightarrow z

    In your case the sample size is still quite small.
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