At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $70 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $3.46. Over the first 32 days she was employed at the restaurant, the mean daily amount of her tips was $71.08. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $70?
H_{0}: μ ≥ 70; H_{1}: μ < 70
H_{0}: μ >70; H_{1}: μ = 70
H_{0}: μ ≤ 70; H_{1}: μ > 70
H_{0}: μ = 70; H_{1}: μ ≠ 70
Reject H_{0} if z > 2.05
Reject H_{1} if z < 2.05
Reject H_{1} if z > 2.05
Reject H_{0} if z < 2.05
Value of the test statistic _____
Do not reject H_{0}
Reject H_{0}
a) Option-C) H_{0}: μ ≤ 70; H_{1}: μ > 70
b) critical value = Z_{0.02} = 2.05
Option-A) Reject H_{0} if z > 2.05
c) Test statistic
= 1.77
d) Option-A) Do not reject H_{0}
e) p-value = P(Z > 1.77) = 1 - P(Z < 1.77) = 1 - 0.9616 = 0.0384
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