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Math Help - power of test random sample

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    power of test random sample

    Maryís cat Baskin requires food with an expected meat content of 80%. From past experience it is known that the meat content in cat food has a normal distribution with standard deviation 5%. Mary buys a crate of cat food for her beloved boy. Baskin decides that he will take a random sample of 10 tins of food, and that he will reject the whole crate if the average meat content (for the sample) is less than 75%. Determine the power of Baskinís test if the expected meat content is actually 77%.
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    Quote Originally Posted by wik_chick88 View Post
    Maryís cat Baskin requires food with an expected meat content of 80%. From past experience it is known that the meat content in cat food has a normal distribution with standard deviation 5%. Mary buys a crate of cat food for her beloved boy. Baskin decides that he will take a random sample of 10 tins of food, and that he will reject the whole crate if the average meat content (for the sample) is less than 75%. Determine the power of Baskinís test if the expected meat content is actually 77%.
    The power of a statistical test is the probability that the test will reject a false null hypothesis (that it will not make a Type II error).

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    i honestly have no idea where to start...i need something to start me off!
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    Quote Originally Posted by wik_chick88 View Post
    i honestly have no idea where to start...i need something to start me off!
    Let Y be the random variable percentage meat content.

    Let \bar{X} be the random variable average percentage meat content of the sample.

    Y ~ Normal (\mu_Y = 77, \, \sigma_Y = 5).

    Therefore \bar{X} ~ Normal (\mu_{\bar{X}} = .... \, \, \sigma_{\bar{X}} = .... ).

    Power = \Pr( \bar{X} < 75).
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