Did I do this correctly?

#1
We suspect that on the average students will score higher on their second attempt at the SAT mathematics exam than on their first attempt. Suppose that we know the changes in score (second try minus first try) follow a normal distribution with standard deviation =60. Here are the results for 40 randomly chosen high school students: -30, 24, 47, 70, -62, 55, -41, -32, 128, -11, -43, 122, -10, 56, 32, -30,-28, -19, 1, 17, 57, -14, -58, 77, 27,-33, 51, 17, -67, 29, 94, -11, 2, 12, -53, -49, 49, 8, -24, 96. Do these data give good evidence that the mean change in the population is grater than zero? State hypotheses, calculate a test statistic and its p-value, and state your conclusion.


Here's my answer.

No, this data does not give good evidence that the mean change is greater than zero.
Ho: u=0 Ha: u>0

z= 11.40 - 0/ (60/sqrt40)= 11.40/9.49= 1.20

P= P(z>1.20)=1- .8849 = 0.12

We would rarely observe that students would score higher on their second attempt on the SAT mathmatics exam.
 

JohnM

TS Contributor
#2
The only thing I would change is to remove your last statement - all you can conclude from this data, is that the average change is not significantly different from 0. You can't make any statements regarding individual scores.