To find the standard error of the sample mean, we need to use the following formula:
[tex]\[ \text{Standard Error} = \frac{\text{Standard Deviation}}{\sqrt{\text{Sample Size}}} \][/tex]
Here's how you can calculate it step-by-step:
1. Identify the Standard Deviation (σ):
According to the given data, the standard deviation of the stride length is 5.65 inches.
2. Identify the Sample Size (n):
The coach is gathering data from 52 team members, so the sample size is 52.
3. Calculate the Square Root of the Sample Size:
The square root of 52 is approximately 7.21.
4. Divide the Standard Deviation by the Square Root of the Sample Size:
We have to divide 5.65 by 7.21 to get the standard error.
5. Perform the Division:
[tex]\[ \frac{5.65}{7.21} \approx 0.783514 \][/tex]
6. Round the Result to the Nearest Hundredth:
Rounded to the nearest hundredth, the standard error is approximately 0.78.
Therefore, the standard error of the sample mean is approximately 0.78.
