Mary has developed a new way of teaching story problems in sixth grade arithmeti
ID: 3152620 • Letter: M
Question
Mary has developed a new way of teaching story problems in sixth grade arithmetic. She used her method on a random sample of 50 sixth graders from her school. An independent random sample of 50 sixth graders was taught to solve story problems by a traditional method. All students were given the same test. Mary's students had an average score x1 = 82 (out of 100 possible points) with standard deviation s1 = 8.5. The other group had an average x2 = 75 with standard deviation s2 = 10.0. Does the new method improve performance on story problems? (Use a 5% significance level.)
Explanation / Answer
Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 = u2
Alternate,new method improve performance on story problems - H1: u1 > u2
Test Statistic
X(Mean)=82
Standard Deviation(s.d1)=8.5 ; Number(n1)=50
Y(Mean)=75
Standard Deviation(s.d2)=10; Number(n2)=50
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =82-75/Sqrt((72.25/50)+(100/50))
to =3.771
| to | =3.771
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 49 d.f is 1.299
We got |to| = 3.77141 & | t | = 1.299
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 3.7714 ) = 0.00022
Hence Value of P0.1 > 0.00022,Here we Reject Ho
We have evidencet that new method improve performance on story problems