Question

Suppose the hypothesis test

*H*0:*μ*=12H0:μ=12

against

*H**a*:*μ*<12Ha:μ<12

is to be conducted using a random sample of *n*=44n=44
observations with significance level set as
*α*=0.05α=0.05.

Assume that population actually has a normal distribution with
*σ*=6.σ=6.

Determine the probability of making a Type-II error (failing to
reject a false null hypothesis) given that the actual population
mean is *μ*=9μ=9.

P(Type-II error) ==

Answer #1

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**Answer:**

ho: u = 12

ha: u < 12

Let us first the critical value of sample mean for Ho: ? = 12. Since test is left tailed so we will reject the null hypothesis when z-score corresponding to sample mean is less than -1.96. So we have

= -1.96 = xcrit - 12/(6/sqrt(44))

xcrit = 10.227113

z = 10.22711329-9/(6/sqrt(44))

z = 0.27724

P(Z>0.27724) = **0.3908**

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