Question

At the time she was hired as a server at the Grumney Family Restaurant, Beth Brigden was told, “You can average $89 a day in tips.” Assume the population of daily tips is normally distributed with a standard deviation of $2.81. Over the first 40 days she was employed at the restaurant, the mean daily amount of her tips was $92.66. At the .01 significance level, can Ms. Brigden conclude that her daily tips average more than $89?

(a)

State the null hypothesis and the alternate hypothesis.

	H0:μ = 89 ; H1: μ ≠ 89
	H0:μ ≥ 89 ; H1: μ < 89
	H0:μ >89 ; H1: μ = 89
	H0:μ ≤ 89 ; H1: μ > 89

(b)

State the decision rule.

	Reject H1 if z > 2.33
	Reject H0 if z > 2.33
	Reject H0 if z < 2.33
	Reject H1 if z < 2.33

(c)	Compute the value of the test statistic. (Round your answer to 2 decimal places.)

Value of the test statistic

(d)

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.)

p-value

Answer 1

(a). Hypothesis:

H0:μ ≤ 89 ; H1: μ > 89

(b). The decision rule:

Reject H0 if z > 2.33

(c). Value of the test statistic = 8.24

(d). Reject H0

(e). P-value = 0.0000