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Probability of Type II error and Power

# Probability of Type II error and Power - (The following...

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Sec. 8.6 Power and probability of Type II error Example – calculating power regarding to z -test for one population mean The manufacture of a new model car claims that a typical car gets 26 mpg. A consumer advocacy group plans to perform the hypothesis test H 0 : μ = 26 mpg H a : μ < 26 mpg at the 5% significance level, using a sample of 30 new cars. Assume that the gas mileages are normally distributed with a standard deviation of 1.4 mpg. (a) Find the probabilities of making a type II error if the true mean gas mileage is (i) 25.8 mpg. (ii)25.0 mpg. (Answer 0.0104) (b) Find the corresponding powers. Exercise Repeat part (a) if H a : μ 26 mpg. (Answer: 0.8713)

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Unformatted text preview: (The following material is not covered in the textbook.) Example – calculating powers for testing hypotheses about proportions Let p denote the unknown probability that a coin comes up heads. The coin is tossed 144 times and the number of heads, x , is observed. (a) What is the rejection region for testing H 0 : p = 0.5 vs. H a : p ≠ 0.5 at the 10% significance level? (b) What is the probability of a Type II error when the true value of p is 0.4? (c) What is the power of this test when the true value of p is 0.4? (d) What is the power of this test when the true value of p is 0.55? (0.3295)...
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Probability of Type II error and Power - (The following...

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