Question 1: Find the z-score
Your data: To test the training program’s claim, you recorded the VAST scores of 10 randomly sampled graduates of the program and you found the sample mean to be 530. Use these sample data to address the training program’s claim that their graduates on average score better than 500 on VAST.
First, calculate a z-score for the sample mean, X, of 530 given that the population standard deviation, s, is 100 and population mean, m, is 500. (Hint: you may view the formula for converting sample means into z-scores here). Which of the following z-scores is correct?
z= 0.00
Incorrect! Based on the formula below, the only way to obtain a z-value equal to 0.0 would be if the sample mean, X, was equal to the population mean, m. In this case, the sample mean of 530 does not equal the population mean (500). Therefore, z = 0.0 is an incorrect answer.
z= 0.09
Incorrect! Check your calculations. Perhaps you multiplied the terms in the denominator.
z= 0.30
Incorrect! You may have forgotten to use the sample size, N, in the denominator of the formula. Note that we are testing a sample mean, not an individual score. Recall, the values for this example are: sample mean (X) = 530, population mean (m) = 500, population standard deviation (s) = 100, sample size (N) = 10.
z= 0.95
Correct! z = .95.
z= 3.00
Incorrect! Did you remember to take the square root of N?
