Question

In this exercise, you will calculate and graph confidence intervals that arise from many samples of the same size drawn from the same population. The aim of the exercise is for you to see what the confidence level means. In this exercise, we will use 95% confidence.

(1) The population will consist of the four values: 5, 10, 15, 50. Enter the data in your calculator and get the mean and population standard deviation.

I am having trouble with this question. My teacher gave us the answers but it doesn't show the work. The correct answers are mean= 20 and population standard deviation= 17.68

(TI-84 calc) When I try and solve this what I do is I put 5, 10, 15, and 50 all in the L1 data in my calculator. After that I do a TInterval test with C-level as 0.95 and List as L1 and press calculate. I end up getting 20 for my mean but Sx= 20.4124... when it should be 17.68. Am I going at this the wrong way and getting the mean just by coincidence?  

Answer 1

Given data are

5, 10, 15, 50

Using the TI-84 calculator:

For calculating the confidence interval of 95%

we must have to first calculate the mean and standard deviation.

NOTE: You may be getting standard deviation as 20.41 because taking as the sample while the given 4 values are population, Be careful!

For getting mean and standard deviation:

Follow these steps-

List all data in the 'L1' column then hit the 'stat' button and under the 'calculator' column select 1-var Stats then hit 'calculate'.

That's it we have got the mean of 20 and a standard deviation of 17.68.

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For calculating confidence t- interval

Follow these steps-

Press "stat" button then under "Tests" column select "Tinterval"

There will be two columns appear "Data" and "Stats"

Under "Data " column set C-level at 0.95

then under "stats" column fee all the mean and variance input

Then press "calculate". That's it. We have calculated the interval.

Again remember given values are population not sample.

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