Widgets come in batches of high quality and low quality. A company orders a batc

Question

Widgets come in batches of high quality and low quality. A company orders a batch of 1000 high quality widgets. Upon arrival the engineer must decide whether the batch is really high quality or if the company was cheated and sent a low quality batch. High quality means that the proportion that work is 0.9 and low quality means the proportion that work is 0.6. The engineer tests a random sample of 30 widgets and will decide that the batch is not high quality if less than 15 work.

i) Determine the size of his test.

ii) Determine the power of his test.

iii) Comment on the values you obtained.

Explanation / Answer

1)

The required sample size is: 32

2)

The power of the test is: 0.78

3)

To compute the power of the test, one offers an alternative view about the "true" value of the population parameter, assuming that the null hypothesis is false. The effect size is the difference between the true value and the value specified in the null hypothesis.

Effect size = True value - Hypothesized value

For example, suppose the null hypothesis states that a population mean is equal to 100. A researcher might ask: What is the probability of rejecting the null hypothesis if the true population mean is equal to 90? In this example, the effect size would be 90 - 100, which equals -10.

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