Question

An athletics coach is interested in quantifying the ability of secondary school athletes at discus throwing. She takes a sample of 13 school athletes and measures the maximum distance achieved by each athlete. The sample mean was 53.8 m, while the standard deviation 7.45 m.

Construct and interpret a 99% confidence interval for the population mean distance achievable by school-age athletes.

Answer 1

To construct a 99% confidence interval for the population mean distance achievable by school-age athletes in discus throwing, we can use the sample mean, standard deviation, and sample size. Using the formula, we find that the 99% confidence interval is approximately (48.65, 58.95).

Step-by-step explanation:

To construct a 99% confidence interval for the population mean distance achievable by school-age athletes in discus throwing, we can use the formula:

Confidence Interval = Sample Mean ± (Critical Value) × (Standard Deviation / √Sample Size)

Given that the sample mean is 53.8 m, the standard deviation is 7.45 m, and the sample size is 13, we need to find the critical value for a 99% confidence level.

Looking up the critical value in a t-distribution table or using a calculator, we find it to be approximately 2.898. Plugging in the values into the formula, we get:

Confidence Interval = 53.8 ± (2.898) × (7.45 / √13)

Simplifying this expression, we get the 99% confidence interval to be approximately (48.65, 58.95). This means that the true population mean distance achievable by school-age athletes in discus throwing is estimated to be between 48.65 m and 58.95 m with 99% confidence.