Need the answer to Part (d) & Part (e). Thank you! (a) Use the operating charact

Question

Need the answer to Part (d) & Part (e). Thank you!

(a) Use the operating characteristic curve to determine the sample size (degrees of freedom) necessary to conduct a two-sided one-sample test for an unknown mean with unknown variance at significance alpha = 0.05 to detect a standard error d = |delta|/sigma greaterthanorequalto 0.5 with power 0.6. (b) Use the operating characteristic curve to determine the sample size (degrees of freedom) necessary to conduct a one-sided one-sample test for an unknown mean with unknown variance at significance alpha = 0.01 to detect a standard error d = |delta|/sigma greaterthanorequalto 0.8 with power 0.8. (c) What sample size is necessary to conduct a two-sided test for an unknown mean with known variance sigma^2 = 1.5 at significance alpha = 0.005 to detect a deviation |delta| greaterthanorequalto 1/10 with power 0.7? (d) For a test with probability of type II error 0.01, what is the corresponding power of that test? (e) For a test with power 0.95, what is the corresponding probability of type II error?

Explanation / Answer

d) type 2 error (beta) = probability of accepting the null hypothesis when it is false

power = 1- beta

power = 1-0.01 = 0.99

e) by same logic above,

probability of type 2 error (beta) = 1-power - 1-0.95 = 0.05

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