Suppose you are in the quality control department of an orange packing company.

Question

Suppose you are in the quality control department of an orange packing company. The bag of oranges says that the mean weight of a bag is 5 pounds. To ensure that the mean does not change from the stated 5 pounds, 10 times a day a random sample (of 30 bags) is taken, the sample mean is evaluated and the hypothesis Ho:= 5 against Hap 5 is tested. Each test is done at the 5% level. Over the course of a month 200 statistical tests are done. Suppose the machine has been functioning properly over this month, (the mean weight of an orange bag is 5 pounds) on average how many times will be null be (falsely) rejected?

Explanation / Answer

total number of test being done n=200

probability of rejecting null falsely p=0.05

therefore average number of times null be falsely rejected =np=200*0.05=10

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