The average cost of tuition, room and board at small private liberal arts colleg
ID: 3200503 • Letter: T
Question
The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term, but a financial administrator believes that the average cost is higher. A study conducted using 225 small liberal arts colleges showed that the average cost per term is $8,745 with a standard deviation of $1,500. Let = 0.05. Calculated z=2.45 Can you prove the claim?
What are the null and alternative hypotheses for this study
What is your conclusion based on p-value?
What is the p-value for this test?
Explanation / Answer
Solution :-
Mean, $8,500 per term
Sample size, n = 225
Mean of sample, $8,745 per term
Standard deviation = $1,500
Given =0.05
z = 2.45
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: Average cost is same as reported, 1 - 2 = 0
Alternative hypothesis:Average cost is higher than what is reported, 1 - 2 0
In order to prove the claim, we compute the p-value from the given z value.
Using online z to p calculator we get,
The P-Value is 0.014286.
The result is significant at p < 0.05.
That is the calculated p-value is less than the assumed value of , which is 0.05.
Therefore, we conclude that we reject the null hypothesis and accept the alternate hypothesis, that is the average cost is higher than what is reported.
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