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    Inferring about population Means

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    In random samples of 12 from each of two normal populations, we found the following statistics:

    Xbar1 = 74 S1= 18
    Xbar2 = 71 S2 =16

    a) Test with α= .05 to determine whether we can infer that the population means differ.
    b) Repeat part a increasing the standard deviations to S1= 210 and S2 =198.
    c) Describe what happens when the sample standard deviations get larger.
    d) Repeat part a with samples of size 150.
    e) Discuss the effects of increasing the sample size.
    f) Repeat part a changing the mean of sample 1 to Xbar1 = 76.
    g) Discuss the effect of increasing Xbar1.

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    Solution
    In random samples of 12 from each of two normal populations, we found the following statistics:

    Xbar1 = 74 S1= 18
    Xbar2 = 71 S2 =16

    a) Test with α= .05 to determine whether we can infer that the population means differ.

    Since sample size is less than 30, but samples are from normal population, we will use z statistics
    Here

    Standard Error can be calculated as under

    Observed value of Z is calculated as under

    It's a two tailed test

    Critical value of Z is (-1.96, 1.96) from the tables of normal distribution

    Since ...

    Solution Summary

    Solution describes the steps in hypothesis testing about population means from two sample statistics. Result are studied with variation in sample means, sample deviation and sample sizes.

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