At the time she was hired as a server at the Grumney Family

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $74 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $4.04. Over the first 36 days she was employed at the restaurant, the mean daily amount of her tips was $75.04. At the 0.02 significance level, can Ms. Brigden conclude that her daily tips average more than $74?

Solution

u=74 s=4.04 n=36 x=75.04 a=0.02

a)

H0: u=74

H1: u>74

b)

critical value = Za/2 = Z0.01 = 2.05

reject H0 if z>2.05

c)

test statistic:

z = (x-u) / (s/sqrt(n))

z = 1.54

d)

since z<2.05

do not reject H0

e)

P-value = P(Z>1.54) = 1 - P(Z<1.54)

= 1 - 0.9382

= 0.0618