Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 12 12 students, taught in traditional lab sessions, had a mean test score of 71.7 71.7 with a standard deviation of 4.8 4.8 . A random sample of 14 14 students, taught using interactive simulation software, had a mean test score of 82.3 82.3 with a standard deviation of 3.8 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 μ 1 be the mean test score for the students taught in traditional lab sessions and μ2 μ 2 be the mean test score for students taught using interactive simulation software. Use a significance level of α=0.01 α = 0.01 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

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

Pooled Variance
sp = sqrt((((n1 - 1)*s1^2 + (n2 - 1)*s2^2)/(n1 + n2 - 2))*(1/n1 + 1/n2))
sp = sqrt((((12 - 1)*4.8^2 + (14 - 1)*3.8^2)/(12 + 14 - 2))*(1/12 + 1/14))
sp = 1.6866

Test statistic,
t = (x1bar - x2bar)/sp
t = (71.7 - 82.3)/1.6866
t = -6.285