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The management at Massachusetts Savings Bank is always conccrned about the quali

ID: 3151734 • Letter: T

Question

The management at Massachusetts Savings Bank is always conccrned about the quality of service provided to its customers. With the old computer system, a teller could server an average of 22 customers per hour. A new system was installed, and a random sample of 70 hours of use had an average of 27 customers served per hour and a standard deviation of 2.5 per hour. Testing at 1% significance, would you conclude that the new system is more efficient than the old system? a) State the hypotheses. b) Determine the test statistic. c) Reject the null hypothesis if d) Determine the value of the test statistic. e) State your conclusion about the new computer system.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   22  
Ha:    u   >   22  
              
As we can see, this is a    right   tailed test.   [ANSWER]

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b)  

We use z distribution as n > 30 here.

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c)
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      
              
Hence, reject Ho when z > 2.326. [ANSWER]

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d)      

Getting the test statistic, as              
              
X = sample mean =    27          
uo = hypothesized mean =    22          
n = sample size =    70          
s = standard deviation =    2.5          
              
Thus, z = (X - uo) * sqrt(n) / s =    16.73320053   [ANSWER]

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e)
              
As z > 2.326, we   REJECT THE NULL HYPOTHESIS.  

Hence, there is significant evidence that the new system is more efficient than the old system at 0.01 level. [CONCLUSION]