Using the TI-Inspire for statistics

TI-Inspire manual 1

Newest version Older version

Real old version

This version works well but is not as

convenient entering letter

TI-Inspire manual 1

Instructions

Ti-Inspire for statistics

General Introduction

TI-Inspire manual 2

TI-Inspire manual 3

General Instructions

Press the On, Off button to go to Home page

Opens a page for calculation. This is different from “scratch pad” above in that it can be saved.

Open a page for entering data in the form of a spread sheet

Open a page for plotting and graphing data.

Opens a page for entering document and texts

Quick calculation page

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Use the middle button to navigate among the choices

To select an option press , in the middle button Press [ Enter] (see below)

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Important If you try to divide numbers TI-Inspire will give you a fraction since a

decimal is only an approximation 1

1 Which I am more than happy to live with

Deleting

Highlight the item or column or number and hit “del”

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Finding Mean, Median and Mode

Step 1) Open list so you can enter your data

Press

Click the above icon A new document opens with Lists & Spreadsheet on the page.

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Enter your data in a column (you could use any column) But usually start with A

Give the column a name using the letter keys

Put name in top row beside the letter

Put NOTHING in this row for now.

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use the arrow to select

the page you want and

then hit “enter” to go to

that page

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Problem: Find the mean of the number of hours of TV watched by a sample of freshmen men

during their first week of college.

35, 28, 29, 31, 36, 26, 23, 34,19

Click [Menu]

Enter the Data in the column

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Give column a title if you wish otherwise it will be known by the letter above it. Generally it is better to give each column a unique title so it can be found easily.

Use alphabet keys at the bottom of the calculator to do this

.

Press Menu

Hit

[Menu]


Choose “4: Statistics”

The choose 1: Stat Calculations

Use arrow on navigator button to move left/ right or up/down


Choose “1: One-Variable Statistics

Step 2) leave “num of lists” on "1" and

and then use Tab to get to [OK]

Leave “Num of Lists” as 1



= mean (pronounced “X bar”) Scroll

down for median and other data

This tells the TI where the data is you want the mean of. columns

Leave these three alone Leave Frequency at 1 and

leave the others blank

This tell the calculator where to put the answers. Choose a column that does not already have data in it because it will override anything that is there

You can also press the arrow at the end and it will give you the names of all thedata sets you have at that time


Clearing column and/ or rows of Data

First columns

Use

Go to

Click the above icon.


use center navigator button to the data entry button which will cause it to highlight.

Click on the letter and this will cause the whole column to highlight of the top of the

column you want to clear

When column highlights

Column will empty

Several rows or several columns at the same time: Drag to select additional rows or columns

Copying rows or columns

Use the same procedure as above to highlight the row or column. When it is highlighted

press [ctrl] C to copy a column or row and [ctrl] V to paste it.

Hold down [ctrl]

and hit [del/clear]


Constructing a Box plot

IMPORTANT: The column you want to turn into a box plot must have a name Add a new number to you list of freshman tv watches. This one watches 56 hours a week and probably will not be here the second semester.

On

Select Graph button to get a graph screen


This box will appear

Click here

Name of several file may appear pick the one you wish to do box plot on


It looks this

[Menu]

Choose 1: Plot type

Choose 2 Box plot


Move the arrow over part of the box or the outlier and it becomes a hand

the number that appears is the where the outliers start. In this case “36 “ is not an outlier but anything greater is

Move the hand to the line in the middle o fhte box and it will give you the median. Inthis

case 30


Move the hand to the bottom of the box and it will give you Q1, etc.

The dot by itself to the left is an outlier and is our 56 hour tv watcher


How to find Standard Deviation Go to

Press Home

List & spread sheet/ Data Entry

Enter data and give the column a name

Click the above icon.


4:Statistics

1: Stat Calculations

1:One Variable Statistics


leave on "1"

to [OK] and press

Press center button or Enter


Tab to the last slot


The [OK]

Tab to [OK]

Leave “Num of Lists” as 1

This tells the TI where the data is you want the mean of. columns

This tell the calculator where to put the answers. Choose a column that does not already have data in it because it will override anything that is there

Leave these three alone Leave Frequency at 1 and

leave the others blank


Sx is the standard deviation for a sample and the one you want to use

You can also press the arrow at the end and it will give you the names of all the data sets you have at that time There are two standard

deviations Sx is for a

sample x is for a

population


One sample Z-test

Local citizens have been concerned that the reading program in the public schools may be inferior . The superintendent hires you to conduct an experiment to investigate. You set a = 0.05 (alpha level) for making your decision. You compare the reading level of current high school seniors to national reading proficient norms which are normally distributed with M = 75 and SD = 16. You administer the reading test to 100 randomly selected high school seniors in your city. The obtained mean of the sample = 72. What is your conclusion?

[On]

[Home]

Calculator button at

bottom [Menu]

6:Statistics 7: Stat Tests 1:zTest Push center


The results are not significantly different. Z(100)=-1.875, p>.05

However, at .060 it’s awful

close to being significantly

different!

National mean

National SD

Our sample mean

Our sample size

Our hypothesis: there is not difference between our sample and the comparison sample


One sample T-tests

The United States has the highest teen pregnancy rate in the western world, despite the fact that US teens are not more sexually active than Swedish teens, Canadian teens, or British teens.

The mean teenage pregnancy rate in the US is 11.85%

The rates for states in the this area

( based on survey of 15-19 year olds)

Arkansas 17.28%

Mississippi 18.75

Louisiana 17.05%

Texas 15.25%

HO: There is no significant difference in the pregnancy rate of the states of Arkansas, Mississippi, Louisiana and Texas compared to the rest of the

nation

HA: There is no significant difference in the mean teenage pregnancy rate of

the four states sample and the US average.

Other Alternative hypothesis are of course possible.


Open a spread sheet

Put the date into column as a list

title it “teen”

then choose 4: Statistics then choose 4:Stat Tests


Choose 2: t Test

It is designed to test a sample against a larger

known mean

Choose “Data “ because you

entered your data into a column on the Spreadsheet

page Click “OK”

µ0: mean you a comparing to

List: is the column where you put the data from your

sample Frequency: always 1

Alternate Hyp: Three hypothesis are possible

A two sided Ha: µ ≠ µ0 My

sample mean is significantly different from the population mean, great or less it doesn’t matter it’s just significantly

different. Ha: µ > µ0 My sample is

greater, bigger, etc. than the

national mean Ha: µ < µ0 My sample is less

smaller, etc. than the national

mean


These results would be reported as There is a significant difference in the pregnancy rate of the states of Arkansas, Mississippi, Louisiana and Texas compared to the rest of the nation. t(3) = 7.29, p <.006. The pregnancy rate for the nation was 11.85 and for the four states in question the average was 17.05, s = 1.43


However, if you are given the mean for the data the procedure is different

The average age of mothers in the US when they give birth to their first child is 25.1.

x = 2.6. The average age of a sample of 200 women from the Arkansas Delta

region is 21.7.

Our hypothesis is: Ha: The age of mothers giving birth to their first child is significantly lower in the Delta region of Arkansas than the national average of the sample is significantly lower than the national average. Ha: µ < µ0

[On]

[Home] Calculator button at bottom [Menu]

:Statistics 7: Stat Tests 1:zTest Push center


Press

4: Statistics 4:Stat

Tests" 2:t-test

choose "Stats" this time

These results would be written: “A significant difference (p<.000)was found in the mean age for mother giving birth to their first child in the Arkansas Delta region than the national average. t (199) = -18.49, p <.000. With the mean for the nation being 25.1 and the mean for the delta region of Arkansas being 21.7.”

Means are usually given in addition to the t scores

National standard deviation

National mean

Sample mean

N in our sample

In this case our hypothesis is that our sample (Delta region) is significantly lower than the

Pick column for results and the [OK]


when the difference is significant.

Two Independent Sample T-Test

This t-test is used when you have two separate sample that you are comparing. (They do not

have to be the same size.) Ie. Rainfall in one city to rainfall in another, female scores on a self-

esteem test compared to males scores on the same test.

The Inspire has a 2-Sample T-Test

Enter the data for the two groups you are comparing in two, usually columns

1 & 2. Give them a title

Honolulu-Average Phoenix-Average San Francisco-Average Little Rock - average

month Avg. month Avg. month Avg. month Ave

January 73 January 54 January 51 January 44

February 73 February 58 February 54 February 46

March 75 March 63 March 55 March 56

April 76 April 71 April 56 April 63

May 78 May 79 May 57 May 71

June 80 June 89 June 59 June 80

July 81 July 93 July 60 July 81

August 81 August 91 August 61 August 83

September 81 September 86 September 63 September 75

October 80 October 75 October 62 October 62

November 75 November 62 November 57 November 54

December 74 December 55 December 52 December 44

Honolulu-Average Phoenix-Average San Francisco-Average Little Rock - average

month Avg. month Avg. month Avg. month ave

Janurary 73 Janurary 54 Janurary 51 Janurary 44

Feburary 73 Feburary 58 Feburary 54 Feburary 46

March 75 March 63 March 55 March 56

April 76 April 71 April 56 April 63

May 78 May 79 May 57 May 71

June 80 June 89 June 59 June 80

July 81 July 93 July 60 July 81

August 81 August 91 August 61 August 83

September 81 September 86 September

63 September 75

October 80 October 75 October 62 October 62

November 75 November 62 November 57 November 54

December 74 December 55 December 52 December 44


Enter Data into columns and title

[menu]

4:Statistics

4:Stat Tests

4:2 Sample t Test

Choose Data is your data

is in columns

Choose stat if you have mean and standard deviation


Pick the two columns of data you wish to compare. Of the four in this case any two can be chosen but only at a time.

Put one name in list 1 and the other in list 2. Order does not matter

Choose Alternative hypothesis (Ha:) from the drop down list •µ1>µ2 the first group is significantly more , faster, greater, etc. than the second group •µ1<µ2 the first group is significantly less than, smaller, etc, than the second group •µ1≠µ2 the difference between group 1 and group 2 is not significant

Leave frequency alone


t(22) = -1.1841, p <.002

Scroll down and you find the means and Honolulu’s mean = 77.25 while Little Rock’s mean temperature = 63.25

Wriitten this way There was a significant difference(p <.002) in th eaverage

temperatures of Little Rock and Honolulu, t(22) = -1.1841, p <.002( s= 3.2) with Honolulu mean temperature being 77.25 and Little Rocks

mean = 63.25 (s = 14.65)

It was said earlier to used pooled unless one standard deviation and more than 2 times which in this case it is. Repeat the statistic usign “non-pooled) The result change only

slightly. t(12.8) = 3.23, p <.004

Since it seems logical that Honolulu has a higher average than Little Rock

choose 1 < 2

If the two standard deviations are similar (neither is more than twice of the other), use pooled


Matched pairs t-test

want to know if subjects have more anxiety after they watch a slasher

flick or after watching the evening news.

I will measure anxiety with a state

anxiety scale. The higher the score the more anxiety.

I will use the same subjects twice but to compensate for “order effect" I will

reverse the order they see the two shows

Subject Slasher flick Evening news

1 4 4

2 5 7

3 3 3

4 8 9

Subject Evening news

Slasher flick

5 5 5

6 4 7

7 3 9

8 9 7

9 2 5


This can be treated in terms of two columns since order is not a factor.

Subject Slasher flick

Evening news

1 4 4

2 5 7

3 3 3

4 8 9

5 5 5

6 7 4

7 9 3

8 7 9

9 5 2

Put Slasher Data in

Column A and news data in Column B

Title each

appropriately Title third column “diff”

In the area just below this title type the

following formula

=a[ ]-b[ ]

Hit enter and the

difference will appear in the column below.

This tell the calculator to subtract column b

from column a dn put the difference in c


Go to Menu 4: Statistics 4: Stat Test 2:t test you are not using the 2 sample t-test because you are measuring the actual difference against “0”

Data method input is “Data

For use “0”

Always choose 0

The two tailed test Put your results in d

use [ctrl]

That will turn ( )

into [ ]


Anova

Doing an ANOVA on the TI is amazing simple if you have been doing t-tests

You wish to determine if College status (Fr, Soph, Jr, Sr) affects the number of time in a

month that a male student “goes out”

“Goes out” is defined as leaving the dorm for reason other than going home, to eat in the

cafeteria, to class, to chapel, business, checking mail, or study. Dating, cruising, hanging

out with the “guys”/"girls" would all be considered “going out

A sample was taken and the number of times during the school week (Mon to Fri) for 24

students over a 9-week period are given in the following table.

Fr Soph Jr Sr

3 6 9 12

5 7 10 13

6 9 15 15

2 37 12 18

1 11 11 15

2 6 10 13

Enter the data in to four columns and title them [Menu] 4: Statistics 4: Stat tests


C: AVOVA

Number of groups is the number of columns. In this case 4

In the previous window, you indicated you had four group. Now you need to give the TI the names of the four groups. And then tell the programs where to put the answer.


F(3, 20) = 3.7, p <.03

You will have to scroll down for the second df, it is called the “dfError”


A source table can also be constructed from the information above The Within data row is filled with the error data from the TI

Source SS df MS F p

Between 413.500 3 137.833 32.685 <.001

Within 84.333 20 4.217

Total 497.833 23


Correlations

Enter the data you want to correlate into two columns in the Data and Spreadsheet. This

would usually be columns A [ ] and B[ ] , title them .

Levels of Anger

Levels of depression

3 23

8 24

4 30

11 45

6 22

7 18

5 16

10 42

7 19

6 24

2 26

Punch [menu]

"4:Statistics"

"1: Stat Calculations"

"4:Linear Regressions(a+bx)

There is also a 3: Linear Regression with the formula (mx+b) This one will give you a correlation

but it will also give you extra data you don’t want to bother with. Avoid it.

X List is usually the factor you

believe affects the second. If you

just believe there is a relationship

either factor can be X

Y List is usually the factor affected

by the X factor. Again if you are just

positing a relationship either factor

can be Y


Leave “Save RegEqu to” alone Leave “Frequency” as “1”

Skip “Category List” and “Include Categories”

Put results in an empty column

r = correlation


Regression

Getting a and b on the TI-Nspire to run a regression

Run a correlation and look again it gives you a and b (see example above)


Chi Square

As an example assume the following Chi Square or matrix

Believes in Santa

Does not Believe in Santa

Undecided about The jolly old man

male 35 43 27

female 43 25 10

First set up a matrix with your numbers

choose calculator page (not scratch pad)


On the calculator page type [35,43,27:43,25,10]→a

The comma is to the left of the “o”

Choose semi-colon

[ctrl] and “(“ will give you the [ ] brackets

The semi-colon is activated by the “?| ”button which produces a number of special symbols

Choose “;”


On the calculator page type [35,43,273,25,10]→a

After you have closed the bracket store the matrix in letter “a” you can store it in a

different letter if “a” is already being used.

The → is the store command “sto→” which is activated

by first hitting “[ctrl]”

[ENTER]


[Menu]

6: Statistics

7: stat tests

8: χ22-way Test

[Enter]

Choose the letter “a” or whatever you designated the matrix as for the “Observed

Matrix:”

[OK]

You now have both χ2 and you p value


Goodness of Fit 1 X

Put observed numbers in column a(and name)

Put expected number in column b ( and name)

Expected can be either

1. Total divided by number of factors; You are saying that all factors will

have equal amounts i.e. In the case of bags of M&M’s you would be

saying that there is an equal number of each color in each bag

There are an average of 35 peanut M & Ms in each package and there are 6 colors

35/6 =5.8

2. A known statistic you are comparing your results to./ ie. We compare the

number of M&M’s, by color, in a sample of bags to the number of each

color the company claims on its website.

Assuming a bag of 35 then by percent it would be 9 blue, 8 orange, 4 green, 5 yellow, 5

red and 4 blue(roughly)

[Menu]

M&M’S PEANUT: 23% cyan blue, 23% orange, 15% green, 15% bright yellow, 12% red, 12% brown.


The bag I opened for this sample included

12 blue

7 orange

3 green,

3 yellow

4 red

5 brown

Enter data into two columns

[menu]

4: Statistics

4: Stat Tests

7: χ2GOF

[ENTER]


“Observed List” is the location of the list your sample produced, your bag in this case, column a “Expected List” is the location of either

1. Total/N 2. Comparison data you

are using 3.

df = number of categories - 1

[OK]

The results gives us our χ2 and probability

Using the TI-Inspire for statistics

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