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chap105

# Thatisitismoredifficulttodetectdifferencesbetweenthenu

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Unformatted text preview: I error and Type II error are inversely related. Lowering the significance level of a test (the probability of a Type I error) increases the chance of a Type II error. • the closer the true value of the population mean μ to the value stated in the null hypothesis, the greater the probability of a Type II error and the lower the power ( 1 − β ) of the test. That is, it is more difficult to detect differences between the null and alternative hypotheses. For example, in the above graph, the probability density function for the sample mean when the true population mean is μ = 5.05 is shifted to the left compared to the PDF when the mean is μ = 5.1 . This increases the the probability of a Type II error. 4 Chapter 10.5 Example: Exercise 10.39, page 361. Assume the population standard deviation is: σ = 3 . From a sample of n = 9 the calculated sample mean is: x = 48.2 . (a) At a 10% significance level, test H0 : μ ≥ 50 against H1 : μ < 50 The test statistic is: z= x − 50 48...
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