10 This exercise is based on summary statistics rather than

10. This exercise is based on summary statistics rather than raw data. This information is typically all that is presented in published reports. You can peform inference procedures by hand from the summaries. Use the conservative Option 2 (degrees of freedom the smaller of n₁ 1 and n₂ 1) for two-sample t confidence intervals and P-values. You must trust that the authors understood the conditions for inference and verified that they apply. This isn\'t always true.

Do education programs for preschool children that follow the Montessori method perform better than other programs? A study compared five-year-old children in a certain city, who had been enrolled in preschool programs from the age of three.

(b) In all, 52 children were assigned to the Montessori school and 114 to other schools at age three. When the children were five, parents of 37 of the Montessori children and 31 of the others could be located and agreed to and subsequently participated in testing. This information reveals a possible source of bias in the comparison of outcomes. Explain why. (Round your answers to the nearest whole number.)

About _______% of Montessori parents participated in the study, compared to about ______% of the other parents.

(c) One of the many response variables was score on a test of ability to apply basic mathematics to solve problems. Here are summaries for the children who took this test:

x

Calculate the test statistic. (Round your answer to three decimal places.)
   t=_________

Solution

b)
Sample 1 : X1 =37, n1 =52, P1= X1/n1=0.712
Sample 2 : X2 =31, n2 =114, P2= X2/n2=0.272
About 72% of Montessori parents participated in the study, compared to about 28% of the other parents.

c)
Test Statistic
X(Mean)=19
Standard Deviation(s.d1)=3.11 ; Number(n1)=30
Y(Mean)=17
Standard Deviation(s.d2)=4.23; Number(n2)=25
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =19-17/Sqrt((9.6721/30)+(17.8929/25))
to =1.963