using the TI30X IIs for confidence intervals

Let's say we have the following statistics from a data set and we want to find the 95% confidence interval for mux, the underlying population's true average value.

n = 36
x-bar = 25.35
sx = 6.78

The degrees of freedom will be n-1 = 35, but 35 is not one of the choices on Table A-3, so we have to go with row 34 instead. The Confidence Level Multiplier for 95%, or CLM95%, is 2.032. If you have a TI-30xIIs, key in the following numbers into your calculator to get the high threshold.

25.35+2.032*6.78/[2nd][x^2]36[enter]

The answer should be 27.64616, which we can round to 27.65.

All we have to do to get the low threshold is to change the + to a -. Key in the following.

[up][right][right][right][right][right]-[enter]

After you key this in, the equation line should look like

25.35-2.032*6.78/sqrt(36

and the answer is 23.05384, which rounds to 23.05.

This says we are 95% confident using this data set that the true average of the underlying population is between 23.05 and 27.65.

Inputting a data set into the TI-30X II s

In the following instructions, I will write comments in this font and the stuff from the calculator in a blocky font called Courier. The things the calculator will put on the screen are in black, while the keys you type in will be in red.

First, you want to be in one-variable stat mode. If you are in stat mode, the word STAT shows up on the output screen in small letters.

Step 0: If you don't see the word STAT on your screen, type the following.

[2nd][DATA][ENTER]

This puts you in stat mode. Before you hit enter, the screen should read

1-VAR 2-VAR

and by pressing enter when 1-VAR is underlined, you go into 1-variable statistics mode. You can skip now to Step 2.

Step 1: If you see the word STAT on the screen, type the following.

[2nd][DATA]

What you will see are the words

1-VAR 2-VAR [left][left]

come up on the screen, and then when you scroll left twice, you will see the word

CLRDATA [ENTER]

underlined. That's when you press enter, which clears out any old data you have.

Step 2: Inputting a data set. The two important buttons here are [DATA] and [STATVAR]. [DATA] lets you start inputting data, and when you are finished pressing [STATVAR] will get you to the statistics associated with the data set you just entered.

One variable statistics in the TI-30X II s are input as a frequency table, a value followed by how many times it shows up on the list. Consider the following list.

20, 20, 19, 18, 18, 17, 17, 17, 17, 17, 16, 16, 16, 16, 16, 16, 16, 15, 15,
14, 14, 14, 14, 14, 13, 13, 13, 13, 13, 12, 12, 12, 11, 11, 11, 11, 11,
9, 9, 8, 7, 7, 4, 4, 4,

[DATA]
x1= 20 [down]
frq= 2 [down]
x2= 19 [down]
frq= 1 [down]
x3= 18 [down]
frq= 2 [down]
x4= 17 [down]
frq= 5 [down]
x5= 16 [down]
frq= 7 [down]
x6= 15 [down]
frq= 2 [down]
x7= 14 [down]
frq= 5 [down]
x8= 13 [down]
frq= 5 [down]
x9= 12 [down]
frq= 3 [down]
x10= 11 [down]
frq= 5 [down]
x11= 9 [down]
frq= 2 [down]
x12= 8 [down]
frq= 1 [down]
x13= 7 [down]
frq= 2 [down]
x14= 4 [down]
frq= 3 [down]
x15= [STATVAR]

The screen will go blank, then show the word CALC for a few seconds, then the statistics for the data set appear. You can use the [left] and [right] buttons to look at different statistics. The number that appears is the underlined statistic. On this list, the numbers are as follows.

Step 3: Reading the statistics of the sample. (Or it could be the parameters of the population, depending on how the data set was defined.)

What you will see on the screen is in black, what keys you will press are in red. The only key in these instructions are the left button, but the right button works for scrolling as well.

n x-bar sx sigmax
45 [left]
n x-bar sx sigmax
13.333333... [left]
n x-bar sx sigmax4.073193967 [left]n x-bar sx sigmax
4.027681991 [left]
sum(x) sum(x^2)
600 [left]
sum(x) sum(x^2)
8730

To get out of the screen showing the statistics, press [CLEAR]. If you press [ENTER] instead, the screen will show the equation line with the symbol of the statistic you were looking at added to whatever equation you were just looking at. This will be useful later in the class when we need the average x-bar and one of the standard deviations, either sx or sigmax, for calculating z-scores.

If you have any questions about how to use one-variable mode on the TI-30 X II s, leave a comment or send me an e-mail.

The basics of the TI-30X II S

The TI-30X II S is the recommended calculator for the class. It has many features that will do some very difficult calculations automatically. In the instructions, any time a key press or series of key presses is discussed, the instructions will be in red in the font called Courier.

One of the most important keys on the calculator is the blue key [2nd] at the upper left. Using this key, almost all the black keys and the bottom row of the white keys have double uses. For example, the

[ON]

button is at the lower left. If you press

[2nd][ON]

that turns the calculator off. Some, but not all the functions on the regular black buttons have an inverse function associated with it by pressing 2nd. For example, the 4th button from the bottom in the left column, with [x^2] on it, will square a number, while if you key in [2nd][x^2], it takes the square root of a number. Be careful. To get a square root, you need to type

[2nd][x^2] 3 [ENTER]

which will give you 1.732050808, while to get 3 squared, you type

3 [x^2][ENTER]

to get 9.

To enter in data sets, we will be using the DATA and STATVAR keys, as well as the four arrow buttons in the upper right. Since the four symbols are not available in the text editor I use for this blog, I shall type [up], [down], [left] and [right] to identify the four buttons.

Getting in and out of STAT mode: There are some words written in a small font below the output line for answers. If you see STAT written on that line, this means the calculator has a current set of data it is storing. If you don't see that word, there is nothing currently stored.

If you don't see STAT: Press

[2nd][DATA]

and the equation line of the output screen will give the choices of 1-VAR and 2-VAR. You can use the [left] and [right] buttons to toggle back and forth. Pick the one you want, then press

[ENTER]

(The first data sets we are going to deal with will be 1-variable applications.)

If you want to start a new data set, press

[2nd][DATA][left]

This gives you the CLRDATA option. If you press

[ENTER]

all data that was stored will be erased.

Now we know how to get in and out of STAT mode and erase old data. Next we will learn how to enter a data set and how to get the parameters or statistics, which is to say some of the important numbers associated with the data set, which could be a population or a sample.