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]
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