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

Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $73 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.38. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $74.23. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $73?

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $73 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.38. Over the first 35 days she was employed at the restaurant, the mean daily amount of her tips was $74.23. At the 0.01 significance level, can Ms. Brigden conclude that her daily tips average more than $73?

Explanation / Answer

The statistical software output for this problem is:

One sample Z summary hypothesis test:
: Mean of population
H0 : = 73
HA : > 73
Standard deviation = 4.38

Hypothesis test results:

Hence,

a) H0: 73 ; H1: > 73; Option D is correct.

b) Reject H0 if z > 2.33; Option B is correct.

c) Test statistic = 1.66

d) Do not reject Ho

e) p - Value = 0.0483

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