Question

Suppose that we are interested to determine whether the mean unemployment duration in state A is different from the mean unemployment duration in state B. Suppose also we collect information from samples of unemployed workers from the two states and track the duration in weeks until they get employment.

The following table summarizes the sample results and the population standard deviations

	State A	State B
Sample Size	64	81
Sample mean unemployment duration (in weeks)	20	23
Population standard deviation of unemployment duration (in weeks)	6.00	6.50

What is a correct setup of the hypothesis for this case?

a) H₀: U_a-U_b =/= 0; H_a: U_a-U_b = 0

b) H₀: U_a-U_b >= 0; H_a: U_a-U_b < 0

_c) H₀: U_a-U_b = 0;  H_a: U_a-U_b =/= 0

_d) H₀: U_a-U_b < 0;  H_a: U_a-U_b >= 0

The test statistic Z = ______

a) -3 b) -2.88 c) 2.68 d) 0.00

P-value = ______

a) 0.9980 b) 0.0500 c) 0.0020 d) 0.0040

At a=0.05, what is your decision?

a) Reject the null hypothesis b) Fail to reject the null hypothesis

Based on your decision at a=0.05, what is your conclusion)

a) State A has an average unemployment duration that is lower than that of state B

b) State A has an average unemployment duration that is greater than that of state B

c) There is no evidence to suggest that the average unemployment durations of the two states are different from each other

d) There is enough evidence to suggest that the average unemployment duration of the two states are different from each other

Answer 1

Ans:

1)Two tailed test

Option c is correct.

2)test statistic:

z=(20-23)/SQRT((6^2/64)+(6.5^2/81))

z=-2.88

3)

p-value=2*P(z<-2.88)=0.0040

4) Reject the null hypothesis

5)There is enough evidence to suggest that the average unemployment duration of the two states are different from each other