A sample of 45 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.10 significance level.
H0: μ = 51
H1: μ ≠ 51
One-tailed test
Two-tailed test
Reject H0 if −1.645 < z < 1.645
Reject H0 if z < −1.645 or z > 1.645
Fail to reject H0
Reject H0
Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.645 and 1.645.
Hence reject H0 if z < -1.645 or z > 1.645
Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (49 - 50)/(5/sqrt(45))
z = -1.34
Fail to reject H0
P-value Approach
P-value = 0.1802
As P-value >= 0.1, fail to reject null hypothesis.
A sample of 45 observations is selected from a normal population. The sample mean is 49,...
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