Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 13 students, taught in traditional lab sessions, had a mean test score of 76.1 with a standard deviation of 3.3 . A random sample of 19 students, taught using interactive simulation software, had a mean test score of 80.9 with a standard deviation of 4.9 . Do these results support the claim that the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software? Let μ 1 be the mean test score for the students taught in traditional lab sessions and μ 2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 2 of 4 :

Compute the value of the t test statistic. Round your answer to three decimal places.

Answer 1

x=76.1

y=80.9

nx=13

ny=19

sx2=3.32=10.89

sy2=4.92=24.01

Combined S.D.

s2=13-1*10.89+ 19-1*24.0113-1+19-1

s2=12*10.89+18*24.0112+18

s2=130.68+432.1830= 562.8630

s2=18.762

s=4.3315

t statistic

Under null hypothesis   H0 : μx=μy              vs       H1 : μx≤μy

t= 76.1-80.9-04.3315*113+119

t=-4.84.3315*0.07692+0.05263

t=-4.84.3315*0.12955

t=-4.84.3315*0.3599

t=-4.81.5589

t=3.079

Calculated t statistic at 30 d.f =2.0422

Here calculated t is greater than tabulated t , Hence we reject H0 at 5% L.O.S.

And conclude that , mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software