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chap105

# 2 chapter 105

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Unformatted text preview: normal distribution can be used to look‐up required probabilities. The ideas can be applied to any other hypothesis testing application – but computer software must be used to find probabilities. 2 Chapter 10.5 The probability of a Type II error can be illustrated with a picture. Consider testing H0 : μ = 5 against the one‐sided alternative H1 : μ > 5 Suppose the true population mean is μ = 5.1 . PDF of X with μ = 5 and μ = 5.1 probability of a Type II error if H0 is true if H1 is true significance level 5 5.1 c d o n o t r e j e c t ← → Reject H0 The probability of a Type II error is the probability that the sample mean is below the critical value c when the true population mean is 5.1. 3 Chapter 10.5 The probability of a Type II error depends on the true value of the population parameter – in this case, the population mean. In practice, the true value of the population mean is unknown. From inspection of the above graph, some general results can be stated. By keeping the sample size and population variance the same then: • the probabilities of a Type...
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