Final answer:
To estimate the mean height of college hockey players with a 95% confidence level and a margin of error of 0.5 inches, a sample of approximately 96 students is required.
Step-by-step explanation:
The population standard deviation for the height of college hockey players is 3.2 inches. If we want to estimate the mean height of college hockey players with a 95% confidence level and a margin of error of 0.5 inches, we can use the formula for sample size:
n = (Z * s / E)^2
Where:
- n is the required sample size
- Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence level corresponds to a Z-score of 1.96)
- s is the population standard deviation (in this case, 3.2 inches)
- E is the desired margin of error (in this case, 0.5 inches)
Substituting the values into the formula, we get:
n = (1.96 * 3.2 / 0.5)^2
Simplifying the equation, we find that the required sample size is approximately 96 students.