T Confidence Interval


Always start each new problem from the home screen

Lets say we want to calculate a 95 % confidence interval for a population mean from some sample data. The sample std. dev. is 6 , and the sample mean is 55. The sample size is 15. In this problem we should use a T-interval not a Z-interval. ( we have a sample < 30 , we do not know the population standard deviation)

On the calculator go to the "TESTS" menu. Press

Arrow right to "TESTS" and down to " 8 : TInterval " (see screen below)


Press (this screen will appear)


Once again we must choose "Stats". Press

Arrow down and change the settings on your screen to match these.

X : 55 , Sx : 6 , n : 15 , C-Level : .95

Highlight "Calculate" and press (you will see this screen)


As we can see from the screen above the 95% confidence interval is (51.677 , 58.323). This means that from repeated samples of this population will get a mean value between 51.677 an 58.323 95% of the time.

Example 4 (Using actual Sample Data)

The duration (in minutes) for a sample of 18 OSCAR telephone registrations is shown below: (begin by typing the data into L1)

2.1   4.8   5.5   10.4   3.3    3.5    4.8   5.8   5.3

2.8   3.6   5.9     6.6   7.8   10.5   7.5   6.0   4.5

What is the point estimate of the population mean? Compute the 98% confidence interval for the population mean.

Again we need to use a T-interval since the sample is less than 30 and of unknown distribution with unknown sigma.

On the calculator we want to go to the "TESTS" menu. So press

Arrow right to "TESTS" and down to "8 : TInterval"

Press
(this screen will appear)

Now we want to highlight "Data" and press


Now the only thing left to change is the "C-Level :". Make sure you change "C-Level :" to .98 then highlight "Calculate" and press
(you will see this screen)


This shows us the 98% confidence interval is (4.178, 7.0109). Once again this means that repeated samples of this population will yield a mean value between 4.178 and 7.0109 98% of the time.