Question

Suppose that a random sample of 17 adult U.S. males has a mean height of 71 inches with a standard deviation of 2.9 inches. If we assume that the heights of adult males in the U.S. are normally distributed, find a 90% confidence interval for the mean height of all U.S. males. Give the lower limit and upper limit of the 90% confidence interval.

Answer 1

To calculate the 90% confidence interval for the mean height of U.S. males, find the appropriate t-score, calculate the margin of error, and add/subtract it from the sample mean to find the lower and upper limits of the interval.

Step-by-step explanation:

To compute a 90% confidence interval for the mean height of all U.S. males using the given sample data (mean height of 71 inches, standard deviation of 2.9 inches, and a sample size of 17), the t-distribution is used since the population standard deviation is unknown.

First, we need to find the t-score that corresponds to the 90% confidence level for 16 degrees of freedom (df = n - 1). Using a t-table or statistical software, we find this value (let's call it t*).

Next, we calculate the margin of error (ME) using the formula ME = t* × (s/√n), where s is the sample standard deviation and n is the sample size. Once we have ME, the confidence interval (CI) is given by mean ± ME.

After calculating the margin of error with the t-score, we plug the values into the confidence interval formula to get the lower limit and upper limit of the interval.