Final answer:
The concept James used by creating a 99% confidence interval to estimate the true mean height of professional basketball players is a Confidence interval. The example also involves hypothesis testing and the interpretation of p-values and z-scores for understanding statistical data about heights.
Step-by-step explanation:
The statistical concept that represents James constructing a 99% confidence interval to estimate the true mean height of current professional basketball players is c. Confidence interval. In statistics, a confidence interval is a type of interval estimate that is used to indicate the reliability of an estimate. Specifically, a 99% confidence interval means we are 99% confident that the true mean height of professional basketball players lies between 76.5 inches and 82.5 inches.
The relevant concepts for statistical analysis in this context include the null hypothesis and alternative hypothesis, as well as the interpretation of a p-value. When the p-value is almost zero, as in the case of the high school students' heights mentioned, it suggests that there is strong evidence against the null hypothesis, supporting the claim that the true mean height is less than 73 inches.
In regards to z-scores, the height of 77 inches has a z-score calculation of -0.5141, indicating that it is 0.5141 standard deviations below the mean height. A z-score of 1.5424 for the height of 85 inches implies it is 1.5424 standard deviations above the mean. A z-score of 3.5 is quite high, translating to a height of 90.67 inches for a basketball player, which is exceptionally tall and thus less likely to be accurate.