Final answer:
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.