Final answer:
Jordan can measure and record the height of each basketball player to gather statistically significant data. Using the z-score formula, he can analyze how individual player heights compare to the team average. The heights, as quantitative continuous data, can be used for both descriptive and inferential statistical purposes.
Step-by-step explanation:
Jordan, interested in the height of basketball players on his school’s team, could ask a statistical question such as, "What is your height?" To collect statistically significant data, he should measure the height of each player in a consistent manner, using the same measuring tool, at the same time of day, and record their heights accurately to ensure precision.
To analyze the data, Jordan could use the z-score formula which standardizes individual data points in relation to the mean and standard deviation of the set. For instance, a player with a height of 77 inches would have a z-score calculated as follows: z = (77 - mean) / standard deviation. This result would show where the player's height falls in relation to the average height of players. Similarly, calculating the z-score for a height of 85 inches would indicate how much taller than average the player is.
If Jordan came across a player with a reported z-score of 3.5, skepticism would be warranted since this suggests a height of over 7.7 feet, which is exceptionally tall and rare even among professional NBA players. In such a case, a practical measurement to verify the player's height would be advisable.
Furthermore, statistical analysis could involve hypothesis testing, using a sample mean and standard deviation to assess whether the mean height of the players is statistically different from a hypothesized value. For example, if the p-value in a certain test is almost zero, this would suggest that the sample data are significantly different from the null hypothesis. In this context, null and alternative hypotheses would need to be clearly stated.
Ultimately, the heights of players constitute quantitative continuous data, which can be analyzed for a variety of descriptive and inferential statistical measures.