1

Test I Marks:
 $$|\ 23\ |\ 20\ |\ 19\ |\ 21\ |\ 18\ |\ 20\ |\ 18\ |\ 17\ |\ 23\ |\ 16\ |\ 19 | $$

Test II Marks:
$$|\ 24\ |\ 19\ |\ 22\ |\ 18\ |\ 20\ |\ 22\ |\ 20\ |\ 20\ |\ 23\ |\ 20\ |\ 18\ |$$

Eleven school boys were given a test in mathematics. They were given one month special classes and the second test was held at the end of it. Do the marks provide evidence that the students were benefited by the special classes?

My attempt:

Using the T-test

$$H_0: μ=0$$

$$H_1: μ>0$$

$$α=0.05$$

$$Degree\ of\ freedom=11-1=10$$

I'm not entirely sure how to proceed after this

Faiq Irfan
  • 1,313
Rutvik Saptarshi
  • 13

1 Answers1

0

Your approach using the T-test does not seem correct to me, since the underlying assumption is that the data is drawn from a normal distribution with unknown variance. The data consists of paired observation (one before and one after the special classes, for each student), and is discrete (i.e. values seem to be in (a subset of) $\{0,1,2,\ldots50\}$).

Using a non-parametric test seems the best thing to do, since these can be used under minimal assumptions. I think the right test to use is the Wilcoxon signed rank sum test, altough extra assumptions on the data may imply another test, i.e. if you assume normality, a T-test might be the right test. If you want to know how to conduct the Wilcoxon signed rank sum test (and the T-test), use Google to look for examples.

Václav Mordvinov
  • 3,268