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14 January, 18:41

Consider the following hypothesis test:H0: u u is less than or equal to 50Ha: u > 50A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use =.05. a. With? x = 52.5, what is the value of the test statistic (to 2 decimals) ? Can it be concluded that the population mean is greater than 50? b. With? x? = 51, what is the value of the test statistic (to 2 decimals) ? Can it be concluded that the population mean is greater than 50? c. With? x? = 51.8, what is the value of the test statistic (to 2 decimals) ? Can it be concluded that the population mean is greater than 50?

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  1. 14 January, 18:56
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    Step-by-step explanation:

    Because we know the population standard deviation, we must use a Z-test.

    Null hypothesis (H0) : μ=50

    Alternative hypothesis (H1) : μ> 50

    The decision rule is:

    z-statistic You must accept the null hypothesis

    z-statistic > Z (z-student table (alpha/2)) - -> You must reject the null hypothesis

    z-statistic formula:

    z = (xbar-m) / (σ / (sqrt (n)))

    xbar: sample mean

    m: hypothesized value

    σ: population standard deviation

    n: number of observations

    a)

    z = (52.5-50) / (8/sqrt (60))

    z = 2.42

    The z-distribution table statistic at 2,5% (alpha/2) significance level is: 1.96 Because z-statistic is greater than the z-table value, we must reject the null hypothesis. It can be concluded that the population mean is greater than 50.

    b)

    z = (51-50) / (8/sqrt (60))

    z = 0.96

    The z-distribution table statistic at 2,5% (alpha/2) significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.

    c)

    z = (51.8-50) / (8/sqrt (60))

    z = 1.74

    The z-distribution table statistic at 2,5% (alpha/2) significance level is the same: 1.96 Because z-statistic is less than the z-table value, it cannot be concluded that the population mean is greater than 50.
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