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Answer:
Since is a two sided test the p value would be:
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
represent the sample mean
represent the sample standard deviation
sample size
represent the value that we want to test
represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
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:
Alternative hypothesis:
The statistic is given by:
(1)
Calculate the statistic
The statistic for this case is given
P-value
The first step is calculate the degrees of freedom, on this case:
Since is a two sided test the p value would be:
And since the p vaue is lower than the significance level we have enough evidence to reject the null hypothesis.