Answer:
We conclude that population mean is equal to 100 at the α=0.01 level of significance.
Step-by-step explanation:
Given information:
Sample size, n=40
Sample mean=104.3
sample standard deviation, s=18.2
We need to check whether the population mean greater than 100 at the α=0.01 level of significance.
Null hypothesis:
[tex]H_0:\mu=100[/tex]
Alternative hypothesis:
[tex]H_1:\mu>100[/tex]
Let as assume that the data follow the normal distribution. It is a right tailed test.
The formula for z score is
[tex]z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]z=\frac{104.3-100}{\frac{18.2}{\sqrt{40}}}[/tex]
[tex]z=1.494263[/tex]
[tex]z\approx 1.49[/tex]
Using the standard normal table the p-value at z=1.49 and 0.01 level of significance is 0.068112.
(0.068112 > 0.01) p-value is greater than α, so we accept the null hypothesis.
Therefore, we conclude that population mean is equal to 100 at the α=0.01 level of significance.
