Question

A teacher is interested if students learning from a new edition of a math textbook have higher or lower scores on a math test. She tests a sample of students, and finds the following scores (higher scores indicate better performance). She doesn’t have scores for all of the students who used the old textbook, but she thinks that on average they score a “4”, and so she decides to compare performance to this value. Here is the data she collects:

9
8
1
2
7
9
10
1
8
8
9

Answer 1

Here, obs T = 2.44 and tab t_{​​​​​​0.05/2;n-1}​ = tab t_{​​​​​​0.025;11-1}= 2.228

Hence we see that, obs T= 2.44 > tab t_{​​​​​​0.025;10}= 2.228

So, we reject the null hypothesis at level alpha=0.05

Conclusion:- from the above calculation we conclude that, learning from a new edition of math textbook have higher or lower scores on a math test.

Note:- here we consider the null hypothesis as the score is same as previous and alternative hypothesis the score is change from previous i.e either higher or lower.