This section of the tutorial assesses your understanding of basic hypothesis testing. For this exercise, you will be asked to calculate a Z-score by hand and draw a conclusion.
Example:
The Graduate Record Exam (GRE) is a standardized test required by many graduate schools/universities for admission. The test contains three sections; verbal, quantitative, and analytical.
GRE scores are often among the most important factors in graduate school admissions. That is, high scores on the GRE make admission more likely. Many companies offer expensive GRE training courses, claiming that their graduates will score better than people who have not taken their class.
Scores on the GRE quantitative section (the section on math) range from 200 to 800. According to the Educational Testing Service, the mean score for people who take the GRE but do not participate in a training courses is 555 with a standard deviation of 139.
A training program boasts that their graduates score higher on average than the population of individuals who do not participate in a training course. That is, the training program claims that their graduates on average will score higher than 555 on the quantitative section. As a budding statistician, you have been hired to test this claim.
To test the training program's claim, you randomly sample the GRE quantitative scores of 10 graduates of the program. This sample of program graduates obtained an average score of 580 on the exam. We can use this sample value to address the training program's claim that their graduates on average score better than 555 on the quantitative section of the GRE.
First, calculate a z-score for the sample mean of 580.
Which of the following z-scores is correct?
a) z = 0.0
b) z = 0.57
c) z = 1.24
d) z = 0.18
e) z = -1.24
f) I'm not sure how to calculate a z-score -- go to a review of z-scores