Question

n the 2021/2022 season, the average points per game scored by players in the whole entire NBA (the population) was 8.24 the standard deviation was 6.33. Here's the data for the Heat only (the sample). Remember, these data are the same as what we have been using in the other assignments. Your job is to determine if sample (the Miami Heat) differs from the whole population (the whole NBA) in the 20212022 season. In other words, are the players on the Miami Heat representative of the rest of the NBA in terms of points per game? Now, you want to test out whether just the 5 highest ranked players on the Heat in 2021 were different from the whole population (from the whole NBA). What is the z value for comparing this new smaller sample to the population?

Answer 1

Main Answer:

The z value for comparing the 5 highest ranked players on the Miami Heat to the whole NBA population in terms of points per game in the 2021/2022 season can be calculated using the formula
`\(z = \frac{\bar{x} - \mu}{(\sigma)/(√(n))}\)`.

Step-by-step explanation:

To determine the z value, where
`\(\bar{x}\)` is the sample mean, (mu) is the population mean, (sigma) is the population standard deviation, and (n) is the sample size, we use the provided information. Given that the average points per game for the whole NBA is 8.24, the standard deviation is 6.33, and the sample size (number of players) is 5 for the Miami Heat, the sample mean
`(\(\bar{x}\))` is needed.

Once the sample mean is calculated, it can be plugged into the formula to find the z value. This z value will indicate how many standard deviations the sample mean is from the population mean, providing insights into whether the 5 highest ranked players on the Miami Heat differ significantly from the entire NBA in terms of points per game.

Understanding the z value and its interpretation is crucial in statistical hypothesis testing. It allows researchers to assess the significance of differences between a sample and a population, providing valuable insights into the generalizability of findings.