A mayoral candidate claims that on average recipients of foo

A mayoral candidate claims that on average recipients of food stamps stay on the program for 12 months. To check this claim, a sociologist obtains records on the length of time participants spend on food stamps assistance program. The sociologist

Solution

a. What are the null and alternative hypotheses in numerical symbols (not in words)?

Let mu be the population mean

Null hypothesis: mu=12

Alternative hypothesis: mu not equal to 12

------------------------------------------------------------------------------------------------------------------

b. What is the test statistic for this test?

Z =(xbar-mu)/(s/vn)

=(12.9-12)/(3/sqrt(100))

=3

------------------------------------------------------------------------------------------------------------------

c. What is the p-value?

It is a two-tailed test.

So the p-value= 2*P(Z>3)=0.0027 (from standard normal table)

------------------------------------------------------------------------------------------------------------------

d. What would you conclude about the null hypothesis at ?=.05?

Since the p-value is less than 0.05, we reject the null hypothesis.

------------------------------------------------------------------------------------------------------------------

                 And what would you conclude about the null hypothesis at ?=.001?

Since the p-value is larger than 0.001, we do not reject the null hypothesis.