In a study of effectiveness one class of second grade children learn with activi
ID: 3082336 • Letter: I
Question
In a study of effectiveness one class of second grade children learn with activities. Another class of second grade children serves as the control and learns without activities. After time the reading skills of all of these children were assessed. Summary is: n x s Activities class: 21 51.48 11.01 No Activities class: 23 41.52 17.15 A 95% confidence interval for the difference in mean reading skill score between the children who learned with activities and the ones who learned without activities is ? (use conservative method for degrees of freedom).Explanation / Answer
Pooled sample variance ={(21-1)*11.01^2+(23-1)*17.15^2}/(21+2… =211.78802 So, pooled sd(s)=14.5529 Here we test H_0: mu_1= mu_2 vs H_A:mu_1 is not equal to mu_2 The test statistic under H0 is t=( xbar_1- xbar_2)/ s(1/n_1 +1/n_2)^(1/2) =2.26755 For the both sided test for 95% CI we have alpha/2=0.025 CI= [ (xbar_1- xbar_2) - t(0.025,df)*s(1/n_1 +1/n_2)^(1/2) , (xbar_1- xbar_2) -+ t(0.025,df)*s(1/n_1 +1/n_2)^(1/2) +1/n_2)^(1/2) For both sided test p value=0.0285 df=degress of freedom= n1+n2-2=42 from t table for alpha=0.025 and df=42 we have ,t=2.0181 So,CI= (1.0956,18.8243)