Question

Iowa has decided to run a quasi-experiment in regard to a new program to reduce unemployment. Officials think that the new program will increase employment rates and earnings. Two hundred recipients are selected; 144 are randomly assigned to an unemployment program, and 81 are assigned to a control group. By follow-up interviews, the state finds out how much outside income per week is earned on average, by each individual with the following results:

	Unemployment Program	Control Group
Mean	$140	$100
Std Dev	132	108
n	144	81

a. Present a hypothesis and a null hypothesis.  
b. Calculate your t-score (involving the overall standard error for the difference of means);
c. estimate your p-value (using n1+n2-2 for d.f.);
d. State a conclusion in plain English.

Answer 1

Let $\mu_1,\mu_2$ denote the average outside income per week of workers assigned to an unemployment program and control group respectively.

Let 1 denotes the sample mean of first sample, s1 denotes the sample standard deviation of first sample and ni denotes the sample size of first sample and 2 denotes the sample mean of second sample, s2 denotes the sample standard deviation of second sample and n2 denotes the sample size of second sample. Here, 1140.00, s1 132.00, n1 144, 2 100.00, s2 108.00, n2 81 The test statistic can be written as: (a 2) t = 1 Sp 1 пj n2 which under Ho follows a t distribution with 223 df. where pooled variance (n1 1)s(n2 1)s 15357.632287 n1tn2- 2 We reject Ho at 0.050 level of significance if P-value < 0.050 or if tobs < to.050,n-1 Now The value of the test statistic 2.323969 associated degrees of freedom 223 The critical value =1.651715 P(t223 < tobs) = P(t223 2.323969) Р value = 0.010514 Since p-value < 0.050 and tobs < teritical = 1.651715, so we reject Ho at 0.050 level of significance Hence, we can conclude that mean for first population is signiifcantly less than mean for second population

d) Conclusion - There is sufficient evidence to support the claim that the new program will increase employment rates and earnings.