# Math Help - significance level

1. ## significance level

A company advertises that its program increases a person’s overall GAMSAT (Graduate Australian Medical School Admissions Test) score by an average of 15 points. To test this claim, an experiment is set up whereby eight subjects are given a diagnostic test that predicts GAMSAT performance, they then take the program, and finally they take the GAMSAT. A predicted score and actual score are recorded for each subject, with the results given in the table below. Test the validity of the company’s claim at a significance level of a = 0.05.

Subject Predicted Score Actual Score
1 50 67
2 84 96
3 74 90
4 67 82
5 88 95
6 70 83
7 57 73
8 71 83

2. Originally Posted by wik_chick88
A company advertises that its program increases a person’s overall GAMSAT (Graduate Australian Medical School Admissions Test) score by an average of 15 points. To test this claim, an experiment is set up whereby eight subjects are given a diagnostic test that predicts GAMSAT performance, they then take the program, and finally they take the GAMSAT. A predicted score and actual score are recorded for each subject, with the results given in the table below. Test the validity of the company’s claim at a significance level of a = 0.05.

Subject Predicted Score Actual Score
1 50 67
2 84 96
3 74 90
4 67 82
5 88 95
6 70 83
7 57 73
8 71 83
Can you use a paired t-test?

3. ok i think i have done the t-test right. i got:
t = 0.892409614 BUT i disregarded the negative from the difference of the means (the mean of X1 was less than the mean of X2) is this right??? now what do i do with the significance level of a = 0.05?

4. Originally Posted by wik_chick88
ok i think i have done the t-test right. i got:
t = 0.892409614 BUT i disregarded the negative from the difference of the means (the mean of X1 was less than the mean of X2) is this right??? now what do i do with the significance level of a = 0.05?
Define $D_i = X_{2i} - X_{1i}$ for i = 1, .....8, the differences between the observations within each pair.

Calculate the mean $\bar{D} = \frac{1}{8} \sum_{i=1}^{8} D_i$ and the standard deviation $S_D^2 = \frac{1}{8-1} \sum_{i=1}^{8} (D_i - \bar{D})^2$ and use the appropriate one sample procedure to complete the inference:

$H_0: ~ \mu_D = 0$
$H_1: ~ \mu_D > 0$

Assuming the differences follow a normal distribution:

$t = \frac{\bar{D} - 0}{S_D/\sqrt{8}} = \, ....$

Use tables to get the critical the critical value of t etc.

You must have examples from class notes or textbook to follow?