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    Statistics help: Null and Alternative Hypotheses

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    In an attempt to improve quality many manufacturers are developing partnerships with their suppliers. A local fast food burger outfit has partnered with its supplier of potatoes. The burger outfit buys potatoes in bags that weigh 20 lbs. It does not wish to accept underweight bags of potatoes. A sample of 40 bags shows an average weight of 19.95 lbs with a standard deviation of 0.1 lbs.

    a. Set up the null and alternative hypotheses to test if the average bag weighs at least 20lbs.
    b. Test your hypotheses using alpha = 0.05
    c. Find the p value
    d. Based on the p value, should the burger outfit accept the shipment of potatoes?

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    Solution Preview

    Please see the attached file.

    The sample mean ( ) = 19.95 lbs.
    The standard deviation (s) of the sample of 40 bags = 0.1 lbs.
    Since there are more than 30 units in the sample we can use z-statistics (normal distribution) for this problem.

    H0: μ 20
    Ha: μ < 20

    α = P(type ...

    Solution Summary

    This solution sets up and tests null and alternative hypotheses for a manufacturer developing a partnership with a supplier.