Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 14 students, taught in traditional lab sessions, had a mean test score of 72.7 with a standard deviation of 6. A random sample of 16 students, taught using interactive simulation software, had a mean test score of 81.6 with a standard deviation of 5.5. 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 μ1 be the mean test score for the students taught in traditional lab sessions and μ2 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 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 H 0. Round your answer to three decimal places.

Step 4of 4: State the test conclusion. (Reject or fail to reject)

Answer 1

Assume that the population variances are equal

Step 1:

Hypothesis:

Step 2:

Test statistic:

t = -4.239

Degrees of Freedom = n1 + n2 - 2 = 14 + 16 - 2 = 28

Critical Value:

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

Step 3:

Decision Rule:

If Test statistic < Critical value, then Reject Ho at % level of significance.

Step 4:

Conclusion:

Test statistic < Critical value, i.e. -4.239 < -1.70,  then 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.