Question

Two sections of a class in statistics were taught by two different methods. Students’ scores on a standardized test are shown in Table 5.12 . Do the results present evidence of a difference in the effectiveness of the two methods? (Use α = 0.05.)

Class A: 74, 97, 79, 88, 78, 93, 76, 75, 82, 86, 100, 94

Class B: 78, 92, 94, 78, 71, 85, 70, 79, 76, 93, 82, 69, 84

Include R code.

Answer 1

Define , : Population mean of scores scored by students in class A

   : Population mean of scores scored by students in class B .

   : Sample mean of scores scored by students in class A .

   : Sample mean of scores scored by students in class B .

   : Sample standard deviation of scores scored by students in class A .

:  Sample standard deviation of scores scored by students in class B

To test :

Test statistic :

where ,

Degrees of freedom = 23

We reject the null hypothesis or H₀ if the observed value of , where ,

The value of the test statistic :  

Critical value :  

Now ,

Hence we accept the null hypothesis or H_{0 .}

Thus we do not have sufficient evidence to support the claim that there exists a difference in the effectiveness of the two methods .