I have invented a tennis shoe that I claim gives basketball players the ability to jump higher. The average max vertical jump height of NBA players is = 38 inches and the standard deviation is = 6 inches. You want to test my shoes to see if they have any effect on jump height and you randomly select a sample of n = 45 NBA players.

1. Based on this information, what is the expected value of the mean of the sampling distribution?

2. What is the standard error of the sampling distribution?

3. If your sample of 45 NBA players has an average jump height while wearing the shoes of M = 40 inches, what is the z-score that represents the location of this value in the sampling distribution?

4. What is the probability of getting this result (40 inches) or greater (enter as a percentage - if your percentage is less than one full percent enter a zero before the decimal point)?

5. Assuming that z-scores greater than +2 or less than -2 are unlikely to occur due to sampling error alone, is this a likely or unlikely result?