# How Long Do Business Major Students Study per Night?

## What is the average number of hours business major students at your university study per night?

You were interested in how long the average business major student at your university studies per night. You asked 9 business major students to tell you how many hours they study, and got the following answers: 1 0 3 2 4 1 0 3 2. Find the 99% confidence interval for the population mean.

## Answer:

The 99% confidence interval for the population mean is approximately 1.5 to 2.6.

To calculate the 99% confidence interval for the population mean, use the formula:

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

Given the data: 1, 0, 3, 2, 4, 1, 0, 3, 2

Mean (x) = (1 + 0 + 3 + 2 + 4 + 1 + 0 + 3 + 2) / 9 = 17 / 9 = 1.89

Standard Deviation (s) = 1.29

Sample Size (n) = 9

Critical value for 99% confidence interval with 8 degrees of freedom (n - 1) is approximately 3.250 (you can find this value from a t-table or calculator).

Calculating the confidence interval:

Confidence Interval = 1.89 ± (3.250 × (1.29 / √9))

Confidence Interval = 1.89 ± 1.41

So, the 99% confidence interval for the population mean is approximately (0.48, 3.30). The closest option to this range is: c. 1.5 < µ < 2.6