Question

You no longer believe that the population standard deviation in the amount of financial aid awarded to this population of students is a known quantity. You therefore will use the standard deviation in the amount of financial aid awarded for a representative sample of students as an estimate of the unknown population standard deviation. You collect award data from a random sample of students once again. This data is shown in appendix one below. Once again, at each of the 5% and 10% levels of significance, is the financial aid award different from $15,000? Again, in your discussion, comment upon the effect of the change in the level of significance on your decision, if necessary. Also, compare, at each level of significance, the results of this portion of the problem to those of the previous part. Account for any difference in your decisions at each level of significance between the two parts of the problem. Make this accounting based not only on a mathematical approach, but rather on a conceptual justification.

$14,200         $16,100         $18,400         $22,000         $15,200         $17,800         $19,300         $19,400         $13,500         $15,500             $21,100         $14,900         $12,000         $  9,500         $14,000             $18,600         $13,800         $17,600         $16,000         $18,500             $19,300         $25,400         $11,500         $  8,000         $  6,000             $17,400         $14,400         $17,500         $12,900         $10,200             $20,400         $13,300         $18,000         $19,800         $12,600             $  7,500         $15,900         $21,800

Answer 1

Given
X bar	15841.67	AVERAGE()
μ0	15000
S	4396.062	STDEV()
n	36

i)

Hypothesis :		α=	0.05
		df	35	n-1
Ho:	μ​ = μ0
Ha:	μ​ not = μ0
t Critical Value :
tc	2.030107928	T.INV.2T(alpha,df)	TWO
Rejection region:
ts	< for -	tc	TWO	To reject
ts	> for +	tc	TWO	To reject
Test :
t	1.148759958	(X bar-μ )/(S/SQRT(n))
P value :
P value	0.258445449	T.DIST.2T(-ts,df)	TWO
Decision :
ts	<	tc	Do not reject H0
P value	>	α	Do not reject H0

Conclusion:

There is not enough evidence to conclude that the financial aid award different from $15,000 at 5% significance level

ii)

Hypothesis :		α=	0.1
		df	35	n-1
Ho:	μ1 = μ0
Ha:	μ​ not = μ0
t Critical Value :
tc	1.689572458	T.INV.2T(alpha,df)	TWO
Rejection region:
ts	< for -	tc	TWO	To reject
ts	> for +	tc	TWO	To reject
Test :
t	1.148759958	(X bar-μ )/(S/SQRT(n))
P value :
P value	0.258445449	T.DIST.2T(-ts,df)	TWO
Decision :
ts	<	tc	Do not reject H0
P value	>	α	Do not reject H0

Conclusion:

There is not enough evidence to conclude that the financial aid award different from $15,000 at 5% significance level