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At the time she was hired as a server at the Grumney Family Restaurant, Beth Bri

ID: 3150556 • Letter: A

Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $87 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.19. Over the first 49 days she was employed at the restaurant, the mean daily amount of her tips was $90.07. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $87?

  

  

  

  

  

   

  

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At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $87 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.19. Over the first 49 days she was employed at the restaurant, the mean daily amount of her tips was $90.07. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $87?

Explanation / Answer

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   87  
Ha:    u   >   87   [ANSWER, C]

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b)
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    +   1.644853627      

hence,

OPTION C: Reject H1 if z > 1.65 [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    90.07          
uo = hypothesized mean =    87          
n = sample size =    49          
s = standard deviation =    3.19          
              
Thus, z = (X - uo) * sqrt(n) / s =    6.736677116 [ANSWER, C]

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d)          

As z > 65,

OPTION A: REJECT HO. [ANSWER]

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e)
              
Also, the p value is              
              
p =    8.10249*10^-12   [very close to 0]