Question

Read and analyze the given problem. Provide a complete solution, Table, and a graph corresponds to the answer.

4. The mean score of the first periodic exam in Statistics is 89 and the standard deviation is 12. One student believed that the mean was less than this, she then randomly selected 34 students and computed their mean score. She obtained that the mean score of 85 at 99% confidence. Test the student belief. Use both method to evaluate

Answer 1

1st method:

t-test:

$t=\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}=\frac{85-89}{12/\sqrt{34}}=-1.94$

$|t|=1.94$

$df=n-1=34-1=33$

Critical value:

$t_{0.99}=2.457$

Since $|t|$ < critical value, we can accept that $\mu<89$

2nd method:

z-test:

$z=-1.94$

p-value:

$P(z<-1.94)=0.02619=0.05238$

Since p-value > $\alpha=1\ \%$ , we can accept that $\mu<89$