Final answer:
To find the range of player heights, identify the smallest and largest height intervals with players on the histogram. The null hypothesis for mean height is 73 inches; a p-value near zero leads to its rejection. Z-scores quantify deviation from the mean, as seen with a 77-inch tall player being -0.5141 standard deviations from the average.
Step-by-step explanation:
To determine the difference in height between the shortest and the tallest player on a basketball team using a histogram, you need to find the height values corresponding to the smallest and largest height intervals that have non-zero frequencies. Unfortunately, the histogram's data is not provided. However, if we had a histogram, you would look at the height intervals on the x-axis and identify the smallest interval with at least one player and the tallest interval with at least one player. The difference in heights of these intervals would give the range, that is, the difference in height between the shortest and tallest players.
Null and alternative hypotheses: To test if the mean height is less than 73 inches, you set up a hypothesis test. The null hypothesis (H0) would state that the mean height is equal to 73 inches (H0: µ = 73), and the alternative hypothesis (Ha) would state that the mean height is less than 73 inches (Ha: µ < 73).
Interpreting the p-value: With a p-value almost equal to zero, we can reject the null hypothesis in favor of the alternative hypothesis. This suggests that there is strong evidence to support the claim that the actual mean height of the players is less than 73 inches.
Z-score calculations give insight into how many standard deviations an individual measurement is from the mean. For instance, a player height of 77 inches has a z-score of -0.5141, indicating that it is 0.5141 standard deviations below the mean height of 79 inches for basketball players.