Question

Do education programs for preschool children that follow the Montessori method perform better than other programs? A study compared five-year-old children in Milwaukee, Wisconsin, who had been enrolled in preschool programs from the age of three. All the children in the study applied to the Montessori school. The school district assigned students to Montessori or other preschools by a random lottery. (a) Comparing children whose parents chose a Montessori school with children of other parents would not show whether Montessori schools perform better than other programs. Why? Parents who want their children to attend non-traditional schools are likely to be wealthier than other parents. O Parents who choose a Montessori school probably have different attitudes about education than other parents. The comparison is legitimate because there is no violation of the conditions for inference. Children who were allowed to attend the Montessori school are likely to be more motivated than children who were not (b) In all, 54 children were assigned to the Montessori school and 112 to other schools at age three. When the children were five, parents of 30 of the Montessori children and 25 of the others could be located and agreed to participate in testing. What possible source of bias in the comparison of outcomes is revealed by this information? O Participation in the testing was according to parents' agreement. The response rate for the children enrolled in Montessori schools is much higher than for the other children. Not all the children in each group participated in the testing. The number of children assigned to the Montessori school is less than half of the numbers of children at other schools.

Answer 1

The provided sample means are shown below:

$\bar X_1$ = 19 $\bar X_2$ ​= 17

Also, the provided sample standard deviations are:

s1 = 3.11 s2​ = 4.19

and the sample sizes are n_1 = 30 and n_2 = 25.

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

X1 - X2 (m1-1)}+(12-1)(1+1)

19-17 (30-13.112-05-114.1 3 0+25-2 1 V = +5) -1

t = 2.03