Using the t-Distribution to Calculate Confidence Intervals - dummies

# Using the t-Distribution to Calculate Confidence Intervals

Use the t-table as needed and the following information to solve the following problems: The mean length for the population of all screws being produced by a certain factory is targeted to be

Assume that you don’t know what the population standard deviation is. You draw a sample of 30 screws and calculate their mean length. The mean for your sample is 4.8, and the standard deviation of your sample (s) is 0.4 centimeters.

## Sample questions

1. What is the 95% confidence interval for the population mean? Round your answer to two decimal places.

The formula for the confidence interval for one population mean, using the t-distribution, is

In this case, the sample mean,

is 4.8; the sample standard deviation, s, is 0.4; the sample size, n, is 30; and the degrees of freedom, n – 1, is 29. That means tn 1 = 2.05.

Now, plug in the numbers:

Rounded to two decimal places, the answer is 4.65 to 4.95.

2. What is the 90% confidence interval for the population mean? Round your answer to two decimal places.