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

ID: 3154938 • Letter: A

Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $71 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.48. Over the first 33 days she was employed at the restaurant, the mean daily amount of her tips was $73.33. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $71?

  

  

  

  

  

   

  

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $71 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.48. Over the first 33 days she was employed at the restaurant, the mean daily amount of her tips was $73.33. At the 0.05 significance level, can Ms. Brigden conclude that her daily tips average more than $71?

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   71  
Ha:    u   >   71   [ANSWER, A]

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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 D: Reject H0 if z > 1.65 [ANSWER]

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c)
              
Getting the test statistic, as              
              
X = sample mean =    73.33          
uo = hypothesized mean =    71          
n = sample size =    33          
s = standard deviation =    4.48          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.987685484 [ANSWER]

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d)          

As z > 1.65, we REJECT HO. [ANSWER]

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e)
              
Also, the p value is, as this is right tailed, using table/technology,              
              
p =    0.001405493   [ANSWER]