Question

For questions 20 – 23 answer all the following questions:

a)State the Null and Alternate Hypotheses

b) Which is the claim?
c) Describe the reject region as left tailed, right tailed or two-tailed.

d) Will you use a z-test or a t-test? What is the critical value?

e) Find the sample statistic.

f) Do you reject or fail to reject the claim? Write out your decision in at least one sentence.

20.   A report by a restaurant reviewer claims that the serving staff, at all casual dining restaurants in New Jersey, receives at least $100 in tips with a standard deviation of $15. Colleen, who works in a casual dining restaurant in New Jersey, believes this claim is wrong. She records her tips over a 30 day, period and finds that they average $93. Using a 1% significance level test the claim.

Answer 1

a)
Null hypothesis, H0: mu >= 100
Alternative hypo, Ha: mu < 100

b)
Here the claim is mu >= 100

c)
This is left tailed test

d)
z-test will be used as population std. dev. is given

P(z < -2.33) = 0.01
Rejection region will be on the left side of the curve because this is left tailed test

Reject H0 if z < -2.33

critical value z = -2.33

e)
test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (93 - 100)/(15/sqrt(30))
z = -2.56

f)
As test statistic < -2.33, reject H0

There is not sufficient evidence to conclude that the serving staff, at all casual dining restaurants in New Jersey, receives at least $100 in tips