Respuesta :
Answer:
[tex]df=n-1=100-1=99[/tex]
Since is a two sided test the p value would be:
[tex]p_v =2*P(t_{(99)}>2.7)=0.0082[/tex]
And since the p vaue is lower than the significance level we have enough evidence to reject the null hypothesis.
Step-by-step explanation:
Data given
[tex]\bar X=2690[/tex] represent the sample mean
[tex]s=360[/tex] represent the sample standard deviation
[tex]n=100[/tex] sample size
[tex]\mu_o =2600[/tex] represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value for the test (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to check if the true mean of interest is different from 2600, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2600[/tex]
Alternative hypothesis:[tex]\mu \neq 2600[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Calculate the statistic
The statistic for this case is given [tex] t_{calc}=2.7[/tex]
P-value
The first step is calculate the degrees of freedom, on this case:
[tex]df=n-1=100-1=99[/tex]
Since is a two sided test the p value would be:
[tex]p_v =2*P(t_{(99)}>2.7)=0.0082[/tex]
And since the p vaue is lower than the significance level we have enough evidence to reject the null hypothesis.
