Question

The following are the marks obtained by 5 students before and after attending coaching classes.

Test whether marks of students has improved after attending coaching classes.

Answer 1

Here marks of same students before and after attending coaching class has given so use paired t-test for equality of me 

H₀ : There is no change in marks of the students before and after attending coaching class, 

i.e., H₀: µ₁ = µ₂ H₁ : 

The marks of the students have improved after attending coaching class 

i.e., H₁ : µ₁, < µ₂ {Left Tail test}

The test statistic is –

Let x and y be the marks of students before and after attending coaching classes

For (n – 1) = (5 – 1) = 4 d.f the lower critical value at 5% level of significance -k = -2.13 

Here t_cal = -0.818 is in acceptance region. 

∴ H₀ is accepted. 

Conclusion : There is no change in the marks of the students before and after attending coaching classes.