Two competing headache remedies claim to give fast-acting relief. An experiment was performed to compare the mean lengths of time required f

Question

Two competing headache remedies claim to give fast-acting relief. An experiment was performed to compare the mean lengths of time required for bodily absorption of brand A and brand B headache remedies. Twelve people were randomly selected and given an oral dose of brand A and another 12 people were randomly selected and given an oral dose of brand B. The lengths of time in minutes for the drugs to reach a specified level in the blood were recorded. The mean and standard deviation for brand A was 21.8 and 8.7 minutes, respectively. The mean and standard deviation for brand B was 18.9 and 7.5 minutes, respectively. Past experience with the drug composition of the two remedies permits researchers to assume that both distributions are approximately Normal. Let us use a 5% level of significance to test the claim that there is no difference in the mean time required for bodily absorption.

Required:
Find or estimate the p — value of the sample test statistic.

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Dulcie 3 years 2021-08-20T21:48:50+00:00 1 Answers 35 views 0

Answers ( )

  1. Adela
    0
    2021-08-20T21:50:47+00:00
    Reply

    Answer:

    t = 0.875

    Step-by-step explanation:

    Given

    Brand A            Brand B

    n_ 1= 12               n_2 = 12

    \bar x_1 = 21.8            \bar x_2 = 18.9

    \sigma_1 = 8.7              \sigma_2 = 7.5

    Required

    Determine the test statistic (t)

    This is calculated as:

    t = \frac{\bar x_1 - \bar x_2}{s\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}

    Calculate s using:

    s = \sqrt{\frac{(n_1-1)*\sigma_1^2+(n_2-1)*\sigma_2^2}{n_1+n_2-2}}

    The equation becomes:

    s = \sqrt{\frac{(12-1)*8.7^2+(12-1)*7.5^2}{12+12-2}}

    s = \sqrt{\frac{1451.34}{22}}

    s = \sqrt{65.97}

    s = 8.12

    So:

    t = \frac{\bar x_1 - \bar x_2}{s\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}

    t = \frac{21.8 - 18.9}{8.12 * \sqrt{\frac{1}{12} + \frac{1}{12}}}

    t = \frac{21.8 - 18.9}{8.12 * \sqrt{\frac{1}{6}}}

    t = \frac{21.8 - 18.9}{8.12 * 0.408}}

    t = \frac{2.9}{3.31296}}

    t = 0.875

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