Question

6. Suppose that the sample unemployment rate for those aged 25–60 is 8% based on a survey of 150 people, while the unemployment rate for those aged 16–24 is 12% based on a survey of 100 people.

(a) Form a 90% confidence interval for the difference between the two population unem- ployment rates.

(b) Construct a test statistic to test the null hypothesis that the two population rates are the same against the alternative hypothesis that the rate is higher in for those aged 16–24, and report the associated P-value.

Answer 1

= 0.08, n1= 150

= 0.12, n2= 100

a)

c= 90%

formula for confidence interval is

Where Zc is the z critical value for c= 90%

Zc= 1.645

−0.105 < P < 0.025

(−0.105 , 0.025)

Thus we get 90% confidence interval as (−0.105 , 0.025)

b)

Ho: P1 = P2

Ho: P1 <  P2

fformula is

z=-1.05

Test statistics = -1.05

P-Value = P(z < -1.05)

using z table we get

P(z < -1.05) = 0.1465

P-Value =0.1465