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Math Help - hypothesis testing

  1. #1
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    hypothesis testing

    hi i need help!

    A manufacturing company makes spray paint. The drying time
    of the paint, in seconds, is known to be approximately normally distributed, with
    mean 90. The people in the research division of the company want to put a new
    chemical ingredient in the paint, which they hope will reduce the drying time.
    In order to investigate this, they make some paint with the new ingredient and
    spray it on 15 surfaces, then record the 15 drying times, in seconds. The sample
    mean of these times is 86 and the sample standard deviation is 4.5.
    Perform an appropriate hypothesis test, at the 5% level of significance, to see
    whether there is evidence that the new ingredient reduces the drying time.

    could sum1 please explain 2 me how to go about this question. thank you
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  2. #2
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    Check your notes

    (Assuming you are a first year at QMUL too) Look at the example from our last statistics lecture as it follows exactly the same process, but with mew=90, standard deviation 4.5.
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  3. #3
    MHF Contributor matheagle's Avatar
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    Your hypotheses are

    H_0:\mu=90 vs. H_a:\mu<90

    where \mu is the mean drying time for the NEW spray.

    Your test statistic is {\bar x- \mu_0\over s/\sqrt{n}}={86-90\over 4.5/\sqrt{15}}.

    The rejection region (of H_0) is (-\infty, t_{14,.05}).

    NOW, if your test statistic falls in the rejection region you reject H_0

    and you accept H_a at \alpha=.05.
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