A random sample of 80 observations produced a sample mean of XXXXXXXXXXFind the critical and observed values of z for each of the following tests of hypothesis using α = .10. The population standard...

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A Test: µ 6= 91 with normal distn
Hypothesis test:
H0 : µ = 91 (Null Hypothesis)
Ha : µ 6= 91 (Alternative Hypothesis, also called H1)
This is two tailed test.
x = 86.5
σ = 7.2
n = 80
Significance Level, α = 0.1
Test statistic or observed value z? = x− µ
σ/
√
n
Test Statistic, z? = 86.5− 91
7.2/
√
80
≈ −5.59017 ≈ −5.59
Test Statistic, z? = −5.59
Rejection Region Approach (Traditional Method)
The Critical Value = zcrit = zα/2 = z0.05 =1.645 (From z table , using interpo-
lation, 1/2 th distance between 1.64 and 1.65 )
Critical Values ±1.645
Rejection Rule:...