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Unformatted text preview: .2 − 50
=
= − 1.8 σn
39 The 10% critical value is zc = 1.282 (since the population variance is viewed as known, the critical value is found in the t‐distribution Appendix Table in the final row for degrees of freedom ∞ ). The results show z < − zc to give evidence to reject the null hypothesis. 5 Chapter 10.5 (b) Find the power of a 10% level test when the true mean is 49. The null hypothesis is rejected for: x − 50 x − 50
=
< − 1.282 σn
39 or, by rearranging, the null hypothesis is rejected for: x < 50 − 1.282 = 48.718 The probability of a Type II error is the probability that the sample mean is not in the rejection region when the true mean is 49. This is stated as: β = P( X > 48 .718 μ = 49 ) This is found as: β ⎛ X − 49 48 .718 − 49 ⎞
⎟
= P⎜
⎜σ n >
⎟
1
⎝
⎠
= P( Z > − 0.282 ) = P( Z < 0.282 )
= 0.61 look ‐ up in Appendix Table 1
The power of the test is: 1 − β = 1 − 0.61 = 0.39 6 Chapter 10.5 Example: Exercise 10.45, page 361. Test H0 : μ ≥ 32 against H1 : μ < 32 Assume the po...
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This note was uploaded on 02/06/2014 for the course ECON ECON 325 taught by Professor Whistler during the Spring '10 term at The University of British Columbia.
 Spring '10
 WHISTLER

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