Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 8 students, taught in traditional lab sessions, had a mean test score of 76.8 with a standard deviation of 4.2 . A random sample of 16 students, taught using interactive simulation software, had a mean test score of 87.8 with a standard deviation of 5.8 . 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 α = 0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 4: State the null and alternative hypotheses for the test.

Step 2 of 4: Compute the value of the t test statistic. Round your answer to three decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.

Step 4 of 4: State the test's conclusion.

Answer 1

We use, Two Sample T test Assuming Equal variances

Given:

n1 = 8, = 76.8, S1 = 4.2

n2 = 16, = 87.8, S2 = 5.8

Step 1:

Hypothesis:

Step 2:

Test statistic:

Step 3:

Degrees of Freedom = n1+n2-2 = 8 + 16 - 2 = 22

Critical value:

..............Using t table

Decision Rule:

Test statistic (t) < Critical value, then is Reject Ho at % level of significance.

Step 4:

Conclusion:

Test statistic (t) < Critical value, i.e. -5.625 < -1.717, that is Reject Ho at 5% level of significance.

Therefore, There is sufficient evidence 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