Notice: For all of the four problems, write down the following clearly: A: Your
ID: 3386160 • Letter: N
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Notice: For all of the four problems, write down the following clearly: A: Your hypothesis B: Your Test statistics C: P-Value D. Conclusion Useful Values: A: For a t distribution with degree of freedom 99.P(t 0.96)=0.177 1. The college bookstore tells prospective students that the average cost of its textbooks is $52. A group of students thinks that the average cost is higher. In order to test the bookstore's claim against their alternative. the students will select a random sample of size 100. The mean from their random sample is $52.80 and standard deviation is $4.50. Perform a hypothesis test at the 5% level of significance and state your decision.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u <= 52
Ha: u > 52 [ANSWER, HYPOTHESES]
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Getting the test statistic, as
X = sample mean = 52.8
uo = hypothesized mean = 52
n = sample size = 100
s = standard deviation = 4.5
Thus, t = (X - uo) * sqrt(n) / s = 1.777777778 [ANSWER, TEST STATISTIC]
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As we can see, this is a right tailed test.
df = n - 1 = 99
Thus, the p value is
p = 1 - 0.961 = 0.039 [ANSWER, P VALUE]
As P < 0.05, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that the average cost of textbooks is greater than $52. [CONCLUSION]
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