Statistics for laboratory scientists

Homework problems for lecture 16

  1. Consider data on the treatment response of 12 mice from strain A and 9 mice from strain B.

    Strain A: 55.2 58.1 41.7 44.9 44.8 48.9 sample mean =48.15
    47.5 48.1 48.4 51.6 40.6 48.0 sample SD =5.06
    Strain B: 48.7 52.6 65.2 70.4 44.2 54.7 sample mean = 55.90
    44.0 66.5 56.8 sample SD = 9.70

    Assume that the measurements from strain A are independent draws from a normal distribution with mean muA and SD sigmaA, and that the the measurements from strain B are independent draws from a normal distribution with mean muB and SD sigmaB.

    Test the hypothesis H0: muA = muB versus the alternative Ha: muA != muB. (By "!=", I mean "not equal to".).

    1. Calculate the P-value for the test.

    2. What do you conclude?

  2. Repeat the above problem for the one-tailed test of H0: muA = muB versus the alternative Ha: muA < muB

  3. Consider data for some measurement on 6 mice before and after some treatment.

    Mouse 1 2 3 4 5 6
    Before 81 101 76 67 125 144
    After 138 210 162 105 259 319
    Difference 57 109 86 38 134 175

    Does the treatment have an effect? Assume that the differences are independent draws from a normal distribution with mean mu and SD sigma.

    Test the hypothesis H0: mu = 0 versus the alternative Ha: mu != 0.

    1. Calculate the P-value for the test.

    2. What do you conclude?

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Last modified: Sun Feb 26 00:14:08 EST 2006