Dr Bliss is comparing the effectiveness of two video gamebas

Dr. Bliss is comparing the effectiveness of two video game-based training modules. He wants to see which module yields better training. He randomly assigned soldiers to two different training modules. Once their training is complete, he tests their performance using a battle simulator. Higher numbers indicate better performance. Training Group A has M = 10, n = 11, and SS = 900; Training Group B has M = 18, n =9, and SS = 750.

What is the alternative hypothesis in both words and statistical notation / symbols?

What is the null hypothesis in both words and statistical notation / symbols?

What is the critical t value?

Compute the test statistic.

Solution

What is the alternative hypothesis in both words and statistical notation / symbols?

Let mu1 be the mean for Training Group A

Let mu2 be the mean for Training Group B

Alternative hypothesis: mu1<mu2 (i.e. Training Group B yields better training)

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What is the null hypothesis in both words and statistical notation / symbols?

Null hypothesis: mu1=mu2 (i.e. there is not different between Training Group A and Training Group B)

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What is the critical t value?

The degree of freedom =n1+n2-2=11+9-2 = 18

It is left-tailed test.

Assume that the significant level a=0.05

The crititcal value is t(0.05, df=18) =-1.73 (from student t table)

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Compute the test statistic.

Training Group A: s1^2= SS/(n1-1) = 900/(11-1) =90

Training Group B: s2^2= SS/(n2-1) =750/(9-1) = 93.75

The test statistic is

t=(xbar1-xbar2)/sqrt(s1^2/n1+s2^2/n2)

=(10-18)/sqrt(90/11+93.75/9)

=-1.86