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A small community college claims that their average class size is equal to 35 students.This claim is being tested with a level of significance equal to 0.02 using the following sample of class sizes: 42,28,36,47,35,41,33,30,39,and 48.Assume class sizes are normally distributed.
-The manufacturer of bags of cement claims that they fill each bag with at least 50.2 pounds of cement.Assume that the standard deviation for the amount in each bag is 1.2 pounds.The decision rule is adopted to shut down the filling machine if the sample mean weight for a sample of 40 bags is below 49.8.Suppose that the true mean weight of bags is 50 pounds.Using this decision rule,what is the probability of a Type II error?
A)0.85
B)0.70
C)0.80
D)0.75

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Quizplus · Accepted Answer

The probability of a Type II error is the probability of failing to reject the null hypothesis when it is false. In this case, the null hypothesis is that the mean weight of bags is 50.2 pounds, and the alternative hypothesis is that the mean weight of bags is less than 50.2 pounds. The decision rule is to shut down the filling machine if the sample mean weight for a sample of 40 bags is below 49.8. If the true mean weight of bags is 50 pounds, then the probability of a Type II error is the probability that the sample mean weight will be greater than or equal to 49.8. This probability can be calculated using the normal distribution with a mean of 50 and a standard deviation of 1.2. The probability of a Type II error is approximately 0.85.

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