Question

Penn State agriculture students raise pigs. They claim that the average pig weighs 525 pounds or more when they are sold. The population variance of weight is 625 pounds². For an appropriate hypothesis test at the α=.01 level, what is the power of a test with this hypothesis using a sample size of n=16 if the true population mean pig weight is 505.875 pounds?

Answer 1

ANSWER::

As we are testing here whether the mean is 525 or more, therefore this is a lower tailed test where null and the alternative hypothesis are given as:

For 0.01 level of significance, we get from the standard normal tables here:

P( Z < -2.326) = 0.01

Therefore the critical value here is -2.326.

The critical sample mean value here is computed here as:

Now the power of the test is computed as the probability of rejecting a false null hypothesis.

Therefore the probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we have here:

Therefore 76.85% is the required power of test here.

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