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Really short question! Please help me to solve part(b), also need the R code, thank you!
Problem 4 [26 points] (Section 2.4): Consider a one-sample z-test (known variance) with hypotheses: Ho: μ lo vs H, μ μο. a/2 where φ(.)Is the CDF of N(0,1), d-layo, and δ is the difference between the true mean and the mean under Ho (a) [10 points] Based on the fact that φ(x) [pdf of N(0,1)] is a decreasing function in x when x> 0, show that (i) for specified values of α and n, (ii) for specified values of α and d, β is a decreasing function of d. β is a decreasing function of n. (b)[16 points] Suppose the true mean is H 13.46. Consider the hypotheses Ho: H14.0 vs H,: μ#14.0 (u-0.05) with variance known at σ2-0.36, what is the minimum sample size to ensure that the probability of Type II error is less than 0.05?
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Answer 4b)

(b) z-statistic = V n(x-13.46)-yM(X-13.46) V0.36 0.6 We reject Ho at level 0.05 if -13.46)1.96. 0.6 Probability of Type 11 error- y(X-13.46)|-1.96|μ = 14 0.6 Vn(x 1414 13.46) 0.6 < 1.961, 14 Φ (1.96-0.9 -Φ (-1.96-0.9泂< 0.05R code: n=10:20 p pnorm(1.96-0.9*sqrt(n))-pnorm(-196-0.9*sqrt(n) k-length(n) m=1k for(i in 1:k) if(plil<0.05) elsel mil-0 N-min(subset(m, m>0)) Out put: Ir

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