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Answer:
The degrees of freedom are given by:
And we want to find a critical value on the t distribution with 61 degrees of freedom who accumulates 0.025 of the area on each tail and the critical value would be
And the rejection region would be
Step-by-step explanation:
Data given and notation
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.
z would represent the statistic (variable of interest)
represent the p value for the test (variable of interest)
State the null and alternative hypotheses.
We need to conduct a hypothesis in order to check if the true mean differs from 11568, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
The degrees of freedom are given by:
And we want to find a critical value on the t distribution with 61 degrees of freedom who accumulates 0.025 of the area on each tail and the critical value would be
And the rejection region would be