What sample size is required to detect an effect of size.What effect size (and mean) can be detected with power.What is the power of the test for detecting a standardized effect of size.We can repeat this calculation for values of μ 1≥ 62.5 to obtain the table and graph of the power values in Figure 2.Įxample 2: For the data in Example 1, answer the following questions: The situation is illustrated in Figure 1, where the curve on the left represents the normal curve being tested with a mean of μ 0 = 60, and the normal curve on the right represents the real distribution with a mean of μ 1 = 62.5. Now suppose that the actual mean is 62.5. The null hypothesis is rejected provided the sample mean is greater than the critical value of x, which is NORM.INV(1 – α, μ, s.e.) = NORM.INV(.95, 60, 1.144) = 61.88. What is the probability of a type II error if the actual mean length is 62.5? The manufacturer wants to check that the mean length of their bolts is 60 mm, and so takes a sample of 110 bolts and uses a one-tail test with α =. We now show how to estimate the power of a statistical test.Įxample 1: Suppose bolts are being manufactured using a process so that it is known that the length of the bolts follows a normal distribution with a standard deviation of 12 mm. the probability that the null hypothesis is not rejected even though it is false and power is 1 – β. As described in Null Hypothesis Testing, beta ( β) is the acceptable level of type II error, i.e.
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