Q. 3.200 - Elementary Statistics

Question

Heights of Basketball Players. This exercise requires that you have first done Exercise $3.199$. In Example $3.12$ on page $109$, we found that, considering the five starting players on Team II a sample of all male starting college basketball players, the mean and standard deviation of the heights are $75 inches$ and $6.2 inches$. respectively. Explain why, numerically, the sample mean of $75 inches$ is the same as the population mean found in Exercise$3.199\left(a\right)$ but that the sample standard deviation of $6.2 inches$ differs from the population standard deviation found in Exercise $3.199\left(b\right)$.

Step-by-Step Solution

Answer

The sample mean and sample standard deviation are estimates of the given population mean and standard deviation.

Step 1: Given information

We need to compare the population mean and standard deviation to the sample mean and standard deviation

Step 2: Explanation

Because the sample mean is a guess at the population mean, it's possible that the two values are equal, but it's also possible that they're not.

Similarly, the sample standard deviation is a guess at the population standard deviation; it's possible that they're the same, but it's also possible that they're not.

It's possible that the means are the same, but the standard deviations aren't .