Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 66 students, taught in traditional lab sessions, had a mean test score of 78.878.8 with a standard deviation of 4.64.6. A random sample of 1212 students, taught using interactive simulation software, had a mean test score of 87.887.8 with a standard deviation of 5.95.9. 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 μ1μ1 be the mean test score for the students taught in traditional lab sessions and μ2μ2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.05α=0.05 for the test. Assume that the population variances are equal and that the two populations are normally distributed.

Step 3 of 4 :  

Determine the decision rule for rejecting the null hypothesis H0H0. Round your answer to three decimal places.

Answer 1

Given that,

For traditional lab sessions : n1 = 6, x1-bar = 78.8 and s1 = 4.6

For interactive simulation software : n2 = 12, x2-bar = 87.8 and s2 = 5.9

The null and alternative hypotheses are,

H0 : μ1 = μ2

Ha : μ1 < μ2

This hypothesis test is a left-tailed test.

Since, population variances are equal,

Degrees of freedom = n1 + n2 - 2 = 6 + 12 - 2 = 16

Using t-table we get, t-critical value at significance level of 0.05 with 16 degrees of freedom is, tcrit = -1.746 (negative because this is a left-tailed test.)

Decision Rule : Reject H0, if t < -1.746