Question

A sample of 50 college students finds their mean credit card debt is $346. The population standard deviation is known to be $108. a. Find a 90% confidence interval for the true mean credit card debt of college students. Round to the nearest cent.

Answer 1

The 90% confidence interval for the true mean credit card debt of college students, with a sample mean of $346 and a population standard deviation of $108 based on a sample of 50 students, is approximately $320.71 to $371.29.

Step-by-step explanation:

To find the 90% confidence interval for the true mean credit card debt of college students, we can use the following formula for the confidence interval when the population standard deviation is known:

Confidence Interval = Sample Mean ± (z-score * (Population Standard Deviation / sqrt(Sample Size)))

The z-score for a 90% confidence interval is 1.645 because we're using the standard normal distribution which has a table or a calculator to find this value. Given that the sample mean is $346, the population standard deviation is $108, and the sample size is 50 students, we can calculate the margin of error as follows:

Margin of Error = 1.645 * ($108 / sqrt(50))

Margin of Error ≈ 1.645 * ($108 / 7.071)

≈ $25.29

So, the confidence interval is:

Lower Bound = $346 - $25.29

≈ $320.71

Upper Bound = $346 + $25.29

≈ $371.29

The 90% confidence interval for the true mean credit card debt of college students is approximately $320.71 to $371.29.