Question

The following data represent a random sample for the ages of 41 players in a baseball league. Assume that the population is normally distributed with a standard deviation of 2.1 years. Use Excel to find the 98% confidence interval for the true mean age of players in this league. Round your answers to three decimal places and use ascending order.

Answer 1

To find the 98% confidence interval for the true mean age of the players in the baseball league, we can use the formula: Confidence Interval = sample mean +- Z * (standard deviation / sqrt(n)). Given that the standard deviation of the population is 2.1 years and the sample size is 41, the Z-value for a 98% confidence level can be found using a standard normal distribution table or a calculator, which is approximately 2.33.

Step-by-step explanation:

To find the 98% confidence interval for the true mean age of the players in the baseball league, we can use the formula:

Confidence Interval = sample mean +- Z * (standard deviation / sqrt(n))

Given that the standard deviation of the population is 2.1 years and the sample size is 41, the Z-value for a 98% confidence level can be found using a standard normal distribution table or a calculator, which is approximately 2.33.

Substituting the values into the formula:

Confidence Interval = sample mean +- 2.33 * (2.1 / sqrt(41))

Calculating the confidence interval:

Confidence Interval = sample mean +- 1.54

Rounding to three decimal places and using ascending order, the 98% confidence interval for the true mean age of players in the league is (sample mean - 1.54, sample mean + 1.54).