In the United States, workers who lose their jobs receive UnemploymentInsurance
ID: 3204130 • Letter: I
Question
In the United States, workers who lose their jobs receive UnemploymentInsurance (UI). One concern with UI is that it might lower unemployedworkers’ incentive to look for new jobs. The State of California decidesto implement a randomized experiment to evaluate the possible disin-centive eect of UI on job search. In the experiment, UI claimants arerandomly assigned to a treatment group and a control group. Workers in the treatment group are oered a cash bonus if they nd a job within13 weeks. Workers in the control group are oered no bonus. You arehired as a consultant by the State to evaluate the eect of the bonuson the duration of unemployment. You obtain the following summaryof the data:
where X1 is the number of weeks that workers in the treatment groupremained unemployed; X2 is the number of weeks that workers in thecontrol group remained unemployed. Let µ1 be the population mean number of weeks of unemployment for the treatment group, and letµ2 be the population mean number of weeks of unemployment for the control group.
(a) What is the approximate distribution of the sample average ¯ X1? Of the sample average ¯ X2?
(b) Derive the 90% condence interval for µ1.
(c) Is µ1 necessarily in the condence interval? Explain.
(d) What is the approximate distribution of ¯X1 ¯X2?
(e) What is the lowest signicance level at which you can reject the null hypothesis that µ1 = µ2?
Variable Obs Mean Standard Deviation Min Max X1 50 10 10 5 150 X2 50 12 10 6 170Explanation / Answer
a)
approximate distribution of the sample average X1= standard deviation/ sqrt(Total number)
=10/sqrt(150)
approximate distribution of the sample average X1=0.816
approximate distribution of the sample average X2= standard deviation/ sqrt(Total number)
=12/sqrt(170)
approximate distribution of the sample average X2=0.920
b)
90% condence interval for µ1
we will use the t distribution with 150-1=149 degree of freedom
90% of values will fall between t=-1.66 and t=1.66
A two sided confidence interval = (10+- 1.66(10/sqrt(150)
=10+-1.355
A two sided confidence interval is then (8.645,11.355).
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