When the Nike Air shoe was first released, it became an instant hit with amateur basketball players as they claimed that they were able to jump higher on Nike Air shoes, compared to other players on a different brand of shoes. To investigate whether this was actually the case a sports-researcher decided to investigate and asked 50 basketballers on Nike Air shoes to participate in his research and to investigate how high these players could jump (wearing their Nike Air shoes). It turned out that on average these players were able to jump 22.5 inches high. 'Pretty impressive' was the conclusion as the researcher was familiar with the population of players that played basketball on a different type of shoe and knew they were only able to jump 21.8 inches! He was also well aware that this population had a standard deviation of 2.8 inches.

Assuming that we're testing two-tailed with an Alpha of 0.05, would we end up rejecting the null hypothesis?

Please calculate the lower bound cut-off for a 90% confidence interval around the sample mean.

We find that the sample mean associated with this off-brand sneaker yields a z of -1.23. What percentile is associated with this z value?

What is the effect size of the difference between the sample and the population mean in the Nike Air example?