Question

In s study done by the Ohio Department of Job and Family Services, it was determined 38 (out of 62) poor children who attended preschool needed social services later in life compared to 49 (out of 61) poor children who did not attend preschool.

A. Does this study provide significant evidence that preschool reduces the need for social services later in life? Do a complete and appropriate hypothesis test using α = .01.

B. Construct a 98% confidence interval estimate of the difference in the proportion of poor children who attended preschool and poor children who did not attend preschool who needed social services later in life. Interpret the practical meaning of the resulting interval estimate, in the context of the problem, in plain English.

Answer 1

Ans:

A)

Given that

Test statistic:

p-value(left tailed)=P(z<-2.32)=0.0102

critical z value=-2.326

As,z=-2.32 is less than equal to critical value,so we reject the null hypothesis.

There is sufficient evidence that preschool reduces the need for social services later in life.

B)

98% confidence interval for p1-p2

=(0.6129-0.8033)+/-2.33*sqrt((0.6129*(1-0.6129)/62)+(0.8033*(1-0.8033)/61))

=0.1904+/-0.1866

=(-0.3770, -0.0037)

As,both limits are negative,we can conclude that preschool reduces the need for social services later in life.