Final answer:
To estimate the mean number of hours spent on required athletic activities by all student-athletes in the conference with a margin of error of 0.5 hours and a 95% confidence level, a sample size of at least 11 student-athletes should be selected.
Step-by-step explanation:
To determine the sample size needed to estimate the mean number of hours spent on required athletic activities by all student-athletes in the conference, we can use the formula for sample size calculation for means.
Sample Size (n) = (Z-score)^2 * (Standard Deviation)^2 / (Margin of Error)^2
Given that the researcher wants to be 95% confident that the sample mean is within 0.5 hours of the population mean, the Z-score for a 95% confidence level is approximately 1.96.
Plugging in the values, we get:
n = (1.96)^2 * (2.3)^2 / (0.5)^2
n = 10.9784, rounding up to 11.
Therefore, a sample size of at least 11 student-athletes should be selected to estimate the mean number of hours spent on required athletic activities with a 95% confidence level and a margin of error of 0.5 hours.