Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 5 students, taught in traditional lab sessions, had a mean test score of 76.3 with a standard deviation of 3.6. A random sample of 9 students, taught using interactive simulation software, had a mean test score of 83.5 with a standard deviation of 3.8. 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 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 H0. Round your answer to three decimal places

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

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 < μ2

2)

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((5 - 1)*3.6^2 + (9 - 1)*3.8^2)/(5 + 9 - 2))*(1/5 + 1/9))
sp = 2.083

Test statistic,
t = (x1bar - x2bar)/sp
t = (76.3 - 83.5)/2.083
t = -3.457

3)
Rejection Region
This is left tailed test, for α = 0.05 and df = n1 + n2 - 2 = 12
Critical value of t is -1.782.
Hence reject H0 if t < -1.782

4)
Reject the null hypothesis