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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