Does the disgruntled teacher have a case against the school system that average salaries are really lower or was their evidence just a fluke?
This is reference to this question:
The Allegheny County, Pennsylvania school district states that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is $60 per day. A disgruntled teacher believes the salary is actually less than this amount. A random sample of five school districts is selected, and the daily salaries (in dollars) are shown. Based on the evidence below, does it look like the disgruntled teacher is correct? Note: In your summary statement, remember to comment on the italicized phrase. You can use α = .10.
60 56 60 55 70
Part A: Solve for ?̅ :
Part B: Solve for s:
Part C: State ho and h1:
Part D: Solve for Critical Values t α/2:
Part E: Calculate
Part F: Apply Decision Rule to determine if ho should be accepted or rejected:
Part G: Summary Statement:
The sample size is n = 5.
X 
X2 

60 
3600 

56 
3136 

60 
3600 

55 
3025 

70 
4900 

Sum = 
301 
18261 
The sample mean Xˉ is computed as follows:
Also, the sample variance s^2 is
Therefore, the sample standard deviation s is
The degrees of freedom is: d.o.f = n−1 = 4
Determining critical value for t with degrees of freedom = 4 and α=0.10.
the critical value is 2.131
The formula for a tstatistic is
since calculated t value = 0.0754 < 2.131 = critical value we fail to reject null hypothesis at 10% level of significance.
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