00:01
Our question says that to study the long -term effect of preschool program support children, researchers design and experiment, they recruited 123 children who had never attended preschool from low -income families in michigan.
00:13
Researchers randomly assigned 62 of the children to attend preschool, paid for the study budget, and the other sister wants to serve as a control group who would not go to the preschool.
00:25
So we have a student, children that went to preschool.
00:30
So preschool, let's just write it here.
00:34
And then we have a new preschool.
00:39
So we call this, i can call this population one and i call this population two.
00:46
So researchers randomly are sent 62 of the children who attend preschool.
00:50
So in this case of ours, our n1 is the cost, excuse me, is the cost of 62.
00:55
And our n2, we have that to be cost to 61.
00:59
N2 is a cost to 61.
01:03
One response variable of interest was the need for social services as aides.
01:07
Adults over a 10 year period 38 children in the base group excuse me 38 children in the preschool group and 49 in the control group have needed social services so in the preschool group we have our 38 children needing social services and in the non - preschool group we have a 49 children x2 needing social services so does the study provide convincing evidence that preschool reduces the later need for social services so our sample proportion p1 cap is going to be cost of 38 over 62 so what will do the math 38 divided by 62 that gives us 0 .61 and p2 cap is going to be 49 divided by 61 and that's going to be 0 .80 so our q1 cap is going to be 1 minus 0 .61 that gives us 0 .39 and our q2 cap is going to be 1 minus 0 .39 and our q2 cap is going to be 1 minus 0 .80 and that is 0 .2020.
02:10
So the first step to perform our hypothesis is to state the null and alternative hypothesis.
02:16
So our h -not is based on the fact that p1 is equal to p2 and the alternative hypothesis is that our p1 is going to be lesser than p2.
02:26
Now after stating the null and alternative hypothesis, the next step is to perform our test statistics.
02:31
And to do so, i am going to be using a z test to perform my test statistics because we have a large sample size right here and then that means our data set is going to be normally distributed so we have our test statistics as z is equals to p1 cap minus p2 cap divided by the square root of we have p1 cap q1 cap divided by n1 plus p2 cap q2 cap divided by n2 so let's substitute the parameters we have our 0 .61 minus 0 .80 divided by the square root of 0 .61 times 0 .39 divided by 62 plus 0 .80 times 0 .20.
03:19
Excuse me.
03:21
Let's take that up.
03:22
D divided by 61.
03:25
So let's bring this here...