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

ID: 3157648 • Letter: A

Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $80 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $2.81. Over the first 42 days she was employed at the restaurant, the mean daily amount of her tips was $82.74. At the 0.10 significance level, can Ms. Brigden conclude that her daily tips average more than $80?

a. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

b. What is your decision regarding H0? Reject H0 Do not reject H0 e. What is the p-value? (Round your answer to 4 decimal places.)

Explanation / Answer

2.

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   80  
Ha:    u   >   80  
              
As we can see, this is a    right   tailed test.      
Getting the test statistic, as              
              
X = sample mean =    82.74          
uo = hypothesized mean =    80          
n = sample size =    42          
s = standard deviation =    2.81          
              
Thus, z = (X - uo) * sqrt(n) / s =    6.319298759   [ANSWER]

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b)

              
Thus, getting the critical z, as alpha =    0.1   , by table/technology,
      
alpha =    0.1          
zcrit =    +   1.281551566      
              
As z > 1.28, WE REJECT HO. [ANSWER]

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e)      
              
Also, the p value is, as this is right tailed,              
              
p =    1.31376*10^-10       [ANSWER]

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