A sample of 31 observations is selected from a normal population. The sample mean is 11, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.05 significance level.
H0: μ ≤ 10
H1: μ > 10
One-tailed test
Two-tailed test
Reject H0 when z > 1.645
Reject H0 when z ≤ 1.645
Reject H0
Fail to reject H0
Solution:
a)
It is a one tail test.
b)
We Reject H0 when Z Score is Large. Therefore, We reject the H0
when Z > 1.645
c)
X = 10 ;
u = 11
s = 3
n = 31,
Therefore,
Z = 1.86
d)
Z = 1.86 > 1.645 ; Hence, We reject the H0
P value for Z = 1.86 is,
p value = 0.0314
Since, P value is less than 0.05; We Reject the null hypothesis.
Hence, we conclude that the mean of the selected sample is less than 11.
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