Question

# Suppose the hypothesis test H0:μ=12H0:μ=12 against Ha:μ<12Ha:μ<12 is to be conducted using a random sample of...

Suppose the hypothesis test
H0:μ=12H0:μ=12
against
Ha: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) ==

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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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