Question

Two teaching methods and their effects on science test scores are being reviewed. A random sample of 9 students, taught in traditional lab sessions, had a mean test score of 71.5 with a standard deviation of 4.1. A random sample of 6 students, taught using interactive simulation software, had a mean test score of 77.9 with a standard deviation of 4.7. 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 3 of 4 :

Determine the decision rule for rejecting the null hypothesis H0

. Round your answer to three decimal places.

Reject H0 if t/or |t|, (<, or >) _________

Answer 1

Solution:

Here is the two sample t test assuming the equal variances.

Claim:  the mean science test score is lower for students taught in traditional lab sessions than it is for students taught using interactive simulation software

i.e. ₁ <  ₂

The hypothesis are

H0:  ₁ =  ₂

H0 : ₁ <  ₂

< sign in H0 indicates that the test is two tailed.

Now , here n₁ = 9 and n₂ = 6

d.f. =  n₁ + n₂ - 2 = 9 + 6 - 2 = 13

Use a significance level of α=0.05

For left tailed , the critical value is   i.e.  

  =   _0.05,13 = 1.771 (using t table)

= -1.771

Step 3 of 4 :

Determine the decision rule for rejecting the null hypothesis H0

Reject H₀ if t < -1.771