Question

A researcher is collecting data about the SEC (Southeastern Conference) and its student-athletes. If the researcher wants to estimate the mean number of hours spent on required athletic activities by all student-athletes in the conference, then how many student-athletes must be included in the sample to be 98% confident that the sample mean is within 0.4 hour of the population mean? Assume the population standard deviation (σ) is 2.41. Use the formula and show all work.

Answer 1

To estimate the mean number of hours spent on required athletic activities by all student-athletes in the SEC with a 98% confidence interval and a margin of error of 0.4 hour, the researcher needs a sample size of at least 15 student-athletes.

Step-by-step explanation:

To estimate the mean number of hours spent on required athletic activities by all student-athletes in the SEC, the researcher needs to determine the sample size needed to achieve a 98% confidence interval with a margin of error of 0.4 hour. The formula to calculate the sample size is:

sample size = (Z-score * population standard deviation) / margin of error

Using the given information, the researcher can plug in the values:

Z-score = 2.33 (from the z-table for a confidence level of 98%)

population standard deviation (σ) = 2.41

margin of error = 0.4

Now, substituting the values into the formula:

sample size = (2.33 * 2.41) / 0.4

sample size ≈ 14.02

Since the sample size must be a whole number, the researcher should round up to the nearest whole number to ensure an adequate sample size. Therefore, the researcher must include at least 15 student-athletes in the sample.