Explain the apparent paradox that even though the difference between the sample mean and μ0 has increased, it is no longer significant.
With reference to Exercise 13.30 below, show that if the first measurement is recorded incorrectly as 16.0 instead of 14.5, this will reverse the result. Explain the apparent paradox that even though the difference between the sample mean and μ0 has increased, it is no longer significant.
13.30. Five measurements of the tar content of a certain kind of cigarette yielded 14.5, 14.2, 14.4, 14.3, and
14.6 mg/cigarette. Assuming that the data are a random sample from a normal population, show that at the 0.05 level of significance the null hypothesis μ=14.0 must be rejected in favor of the alternative μ is not equal to 14.0.
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