Answer:
[tex]z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29[/tex]
Step-by-step explanation:
information given
[tex]\bar X=10.6[/tex] represent the sample mean
[tex]\sigma=4.1[/tex] represent the population standard deviation
[tex]n=45[/tex] sample size
[tex]\mu_o =12[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test
Hypothesis to test
We want to test if the true mean is less than 12, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 10[/tex]
Alternative hypothesis:[tex]\mu < 10[/tex]
The statistic is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
We can replace in formula (1) the info given like this:
[tex]z=\frac{10.6-12}{\frac{4.1}{\sqrt{45}}}=-2.29[/tex]
