The mean weight for a typical bunch of bananas in grocery stores is 3 point 5 4 pounds. The owner of a grocery store will reject a shipment of bananas if the mean weight of the banana bunches is less than 3 point 5 4 pounds. The owner randomly selects and weighs 30 bunches of bananas. A significance test at an alpha level of alpha is equal to 0 point 0 5 tests the hypotheses ratio of cap h sub 0 to mu is equal to 3 point 5 4 pounds; ratio of cap h sub alpha to mu is less than 3 point 5 4 pounds. What is a Type II error in this situation?
Answer
A
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is less than 3 point 5 4 pounds when the true mean weight is actually not less than 3 point 5 4 pounds.
B
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is less than 3 point 5 4 pounds when the true mean weight is less than 3 point 5 4 pounds.
C
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3 point 5 4 pounds when the true mean weight is not less than 3 point 5 4 pounds.
D
Based on the sample mean, the owner concludes that the mean weight of all of the bunches of bananas is not less than 3 point 5 4 pounds when the true mean weight is actually less than 3 point 5 4 pounds.
Explanation
A Type II error occurs when the null hypothesis is not rejected even though the alternative hypothesis is true. Here, that means concluding the mean weight is not less than 3.54 pounds when the true mean is actually less than 3.54 pounds. This is choice D.
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