A. A recent survey indicated that the average amount spent for breakfast by busi

Question

A. A recent survey indicated that the average amount spent for breakfast by business managers was $7.58 with a standard deviation of $0.42. It was felt that breakfasts on the West Coast were higher than $7.58. A sample of 81 business managers on the West Coast had an average breakfast cost of $7.65. At = .05, is this difference significant?

Calculate the test statistic.

B. Nationally, students pay a mean of $380 per student on books per semester. In a sample of 55 students at Ex Pensive University their average cost was $405 with a standard deviation of $80.

Calculate the test statistic.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   7.58  
Ha:    u   >   7.58  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    7.65          
uo = hypothesized mean =    7.58          
n = sample size =    81          
s = standard deviation =    0.42          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.5   [ANSWER, TEST STATISTIC]      

Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      

              
As z < 1.6449, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Hence, this difference is not significant at 0.05 level. [ANSWER]

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