Notice For all of the four problems write down the following

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.

Solution

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]