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BASICS: USING THE TI-83 CALCULATOR
KENKEL NOTES:
LINK FOR VARIOUS TI CALCULATOR HANDBOOKS:
http://education.ti.com/educationportal/appsdelivery/download/
download_select_product.jsp?cid=us&displaymode=G&contentpaneid=17
TURN THE CALCULATOR ON
1. Press ON
TURN THE CALCULATOR OFF
1. Press 2ND
2. Press OFF
((OFF is above the ON key)
TO ADJUST THE CONTRAST
When you turn on the calculator, you may get a blank screen. Probably, you need to adjust the screen
contrast. Otherwise, get new batteries.
1.
Press 2ND
2.
Press up arrow to DARKEN, down arrow to BRIGHTEN
HOW THE KEYS WORK
1. Each key has an option on its face. To select this option, just press the key
2. Each key has a second option listed above the key on the left. To select this option, press 2ND, then
press the key.
3. Each key has a third option listed above the key on the right. To select this option, press the ALPHA
key, then press the key.
MOVING AROUND ON A SCREEN
Frequently, after pressing a key, a menu of numbered options will appear on the screen. You can move the
cursor onto a desired choice by using the UP, DOWN, RIGHT, or LEFT arrows.
SELECTING OPTIONS
Frequently, after pressing a key, a menu of numbered options will appear on the screen. There are two
ways to select your choice:
1. Type the number of your choice
OR
2. Move the cursor onto the desired option and press ENTER
TO CLEAR THE SCREEN
Press CLEAR
(You may need to press CLEAR several times.)
CHAPTER 4: DESCRIPTIVE STATISTICS
HOW TO ENTER DATA INTO THE STAT EDITOR
The STAT editor is BY FAR the most useful tool for saving time when solving statistics problems.
First, we need to learn how to enter data into the STAT editor. Then, we can let the calculator do all the
tedious calculations that are required in statistics.
Suppose we want to enter the following five values of X into the STAT editor:
X
25
10
20
15
5
1. Press the STAT key
The screen shows a list of options, and the cursor always highlights option1: Edit. (This is the
default, so the cursor will always start here.) Whenever you want to see the data in the editor or put
new data into the editor, select the 1: Edit option.
2. Press ENTER
Now the STAT editor appears showing three columns with headings L1, L2, and L3. There are
actually six columns for data. By moving the cursor to the right, you can verify this.
We want to enter the values of variable X into column L1. (You can put the data into any of the six
columns if you wish, but L1 is the default column.).
If your screen shows that you already have some values typed into column L1, you need to delete
them. To do this, move the cursor onto the L1 symbol at the top of the column and press CLEAR.
Then press ENTER. Now the L1 column should be blank.
Now we are ready to enter the five values listed above. The cursor will be in the first position in
column L1.
3. Type 25 and press ENTER
(The value 25 now appears in the first position and the cursor moves to the second position in
column L1. Type each remaining value followed by ENTER. Thus, you should type the following
10 ENTER
20 ENTER
15 ENTER
5 ENTER
This completes the entry of the five values into column L1
TO EXIT THE STAT EDITOR
Suppose you want to exit the STAT editor and get back to the regular calculator.
1. Press 2ND
2. Press QUIT. (The option QUIT is located above the “MODE“ key.)
Whenever you exit the STAT editor, all the data will remain in the same column as when you exited,
(even if you turn off the calculator).
TO CORRECT TYPING ERRORS IN THE STAT EDITOR
1. To REPLACE an incorrect value, move the cursor onto the incorrect value, retype the correct value, and
press ENTER
2. To DELETE an unwanted number, move the cursor onto the unwanted number and press DEL
3. To INSERT an additional number into the middle of a list, move the cursor onto the desired place in the
list
Press 2ND
Press INS
The value 0 will now appear in the desired location in the list. Type the number to be
inserted and press ENTER
EASIEST METHOD OF DELETING DATA FROM ONE COLUMN IN THE STAT EDITOR
There are several ways to clear data in the STAT editor. The following is the easiest and fastest method.
Suppose you want to delete the data that are in any column, say column L2.
1. Press STAT
Cursor will highlight EDIT
2. Press ENTER
3. Move the cursor onto the name L2 at the top of column L2
4. Press CLEAR
5. Press ENTER
The data in column L2 are now deleted.
FASTEST WAY TO DELETE ALL DATA FROM THE STAT EDITOR
1. Press 2ND
2. Press MEM
(The MEM key is above the “+” key.)
The screen now shows a list of options.
2. Move the arrow onto option 4: ClrAllLists
OR. Alternatively, type the number 4 to select the desired option
3. Press ENTER
The screen shows ClrAllLists
4. Press ENTER
The screen now shows Done
All the data in all the columns in the STAT editor have been deleted.
ALTERNATIVE METHOD OF DELETING DATA FROM ONE COLUMN (SAY, COLUMN L2)
1. Press STAT
2. Move cursor onto option 4: CLRLST
3. Press ENTER
4. Press 2ND L2
(L2 is above the “2” key)
5. Press ENTER
The data in column L2 are now deleted
CHAPTER 4: DESCRIPTIVE STATISTICS
CALCULATE THE MEAN, STANDARD DEVIATION, MEDIAN, ETC. USING THE STAT EDITOR
1. Insert the values 25, 10, 20, 15, and 5 into column L1 in the STAT editor. After entering the data, the
screen should look like this:
L1
L2
L3
25
10
20
15
5
To calculate the mean and standard deviation of the X values, proceed as follows:
1. Press STAT
2. Move the cursor onto option CALC
The screen shows a list of options
3. Move cursor onto option 1: 1-Var Stats
4. Press ENTER
Now the screen shows: 1-Var Stats
4. Press 2ND L1
(L1 is above the “1” key)
5. Press ENTER
This tells the calculator to calculate various descriptive statistics using the values located in column
L1 (which is the default column).
SHORTCUT METHOD WHEN THE DATA ARE IN COLUMN L1
(Column L1 is the default column. Whenever your data are in L1, you can omit step 4 above and still get the
same results. When calculating descriptive statistics, the calculator will always use the data in column L1
unless instructed otherwise. If the data you want to analyze are in, say, column L2, then replace step (4) by
4. Press 2ND L2
5. Press ENTER
Similarly, if the data values were in column L3, you’d press 2ND L3 and then press ENTER
Now, some of the results appear on the screen
Xbar = 15; sumX = 75; sumX2 = 1375; Sx = 7.90569415; sigmaX = 7.071067812
To see more results, use the down arrow to observe
minX = 5, Q1 = 7.5; med = 15; Q3 = 22.5; maxX=25
Note that the calculator found the median even though you did not sort the data into order.
Also note that the calculator does not know if you have a sample or a population of data. Thus, the
calculator provides both a population and a sample standard deviation. It is your job to determine
which value is appropriate.
SORTING DATA INTO ASCENDING ORDER
In order to calculate percentiles, the researcher needs to put the data into ascending order from lowest to
highest. Here’s how to do this.
1. Insert your data into the STAT editor as described previously. Put your data into L1. After the data are
in column L1, proceed as follows:
2. Press STAT
A screen appears showing a list of options.
3. Move cursor onto option 2: SortA(
4. Press ENTER
Now the screen shows 2: SortA(
5. Press 2ND L1)
(The closing parenthesis is optional and can be skipped)
This tells the calculator to sort the data that are in column L1.
6. Press ENTER
Now the data in L1 are rearranged, lowest to highest. To see the data, press STAT and then press ENTER
CHAPTER 4: OPTIONAL
CALCULATE THE DEVIATIONS FROM THE MEAN
Use the data from the previous example
L1
L2
L3
25
10
20
15
5
L4
L5
L6
Step 1. To calculate the deviations from the mean, we first need to calculate the mean. To calculate the
mean of the data in column L1, use the CALC option as described on the previous page to calculate the
mean of the data in L1. The mean is 15
Step 2. Now we are ready to calculate the deviations from the mean (X – 15)
1. Press STAT
Cursor will always highlight EDIT
2. Press ENTER
3. Move the cursor onto the name L2 at the top of column L2
4. Press 2ND L1 – 15
5. Press ENTER
(This tells the calculator to take all the values in column L1, subtract 15 from each value, and put the
results in column L2. Thus, this calculates the deviations from the mean (X - 15) and puts these
deviations in column L2)
Now the editor looks like this. The values in L2 are the deviations from the mean, i.e., (X - XBAR).
L1
L2
L3
25
10
10
-5
20
5
15
0
5
-10
CHAPTER 4: OPTIONAL
CALCULATE THE SUM OF THE DEVIATIONS FROM THE MEAN
In class, we proved that the sum of the deviations from the mean must be zero. Let us calculate the sum of
the values in column L2 and check that the sum is zero.
1. Press STAT
Cursor highlights EDIT
2. Move the cursor onto option CALC
The screen highlights option 1: 1-Var Stats
3. Press ENTER
The screen shows "1-Var Stats"
We want the sum and mean of the values in column L2
4. Press 2ND L2
(because we want descriptive statistics for column L2)
5. Press ENTER
The screen shows sumX = 0, XBAR = 0; etc. That is, the sum and mean of the values in column L2
is 0. Thus, the deviations from the mean sum to zero.
CALCULATE THE ABSOLUTE VALUES OF THE DEVIATIONS
The deviations from the mean are listed in column L2. Let us put the absolute values of the deviations in
column L3.
1. Press STAT
The cursor highlights EDIT
2. Press ENTER
3. Move the cursor onto L3 at the top of column L3
4. TI-82 ONLY
Press 2ND ABS 2ND L2 ENTER
(This calculates the absolute values of column L2 and puts them in column L3)
(On the TI-82, the ABS option is on top of the X-1 key)
TI-83 OR TI-83 PLUS ONLY
After step 3, the cursor will be on the L3 at the top of column L3
4. Press 2ND CATALOG
(CATALOG is located above the "0" key on the keyboard)
The screen will show the cursor pointing at option abs(
5. Press ENTER
6. Press 2ND L2
7. Press ENTER
(This calculates the absolute values of column L2 and puts them in column L3)
Now the STAT editor looks like this. The values in L3 are the absolute deviations from the mean.
L1
L2
L3
25
10
10
10
-5
5
20
5
5
15
0
0
5
-10
10
CHAPTER 4: OPTIONAL
CALCULATE THE MEAN ABSOLUTE DEVIATION
The mean absolute deviation is the average (or mean) of the values in column L3.
1. Press STAT
The cursor highlights EDIT
2. Move cursor onto CALC
Cursor highlights option 1: 1-Var Stats
3. Press ENTER
The screen shows "1-Var Stats”
We want the mean of the values in column L3
4. Press 2ND L3
5. Press ENTER
The screen shows XBAR = 6, sumX = 30, etc. That is, the mean of the values in column L3 is 6.
Thus the MEAN ABSOLUTE DEVIATION = 6.
CHAPTER 4: OPTIONAL
CREATE A HISTOGRAM
1. Enter a column of data in column L1 of the STAT editor.
2. Press WINDOW
The screen now shows a list of values that need to be set
3. Xmin is the lower bound of your histogram
Type a value and press ENTER
4. Xmax is the upper bound of your histogram
Type a value qand press ENTER
5. Xscl is the desired width of each class interval
Type a value and press ENTER
6. Ymin is the lower bound for a class frequency
Type 0 and press ENTER
7. Ymax is the highest frequency that will be shown on the graph
Type a value and press ENTER
8. Press 2ND STATPLOT
STATPLOT is above the “Y=“ key
The screen now shows a list of options that need to be chosen
Put the cursor on Plot 1 and Press ENTER
Put the cursor on option On and press ENTER
Put the cursor onto the third figure which is the Histogram symbol and press ENTER
Make sure Xlist is L1 and Freq is 1
8. Press GRAPH
A histogram now appears on the screen.
If you do not like the appearance of the histogram, go back to the WINDOW option and change the
values for Xscl and or Ymax. Then press GRAPH again to see the new histogram.
9. To determine the number of data values in each class, press the TRACE key. Move the cursor to the
right or left with the arrow key to see the class frequency for any class. As you move the cursor, the screen
will list the lower and upper bound for each class and the class frequency for each class.
CHAPTER 5:
POWERS, FACTORIALS, PERMUTATIONS AND COMBINATIONS
POWERS
EXAMPLE: Calculate 53 = 5 x 5 x 5 = 125
1. Press 5
2. Press ^
3. Press 3
4. Press ENTER
(Result is 5^3 = 125)
CALCULATE A SQUARE ROOT
EXAMPLE: Calculate the square root of 144
1. Type 144
2. Press ^
3. Type .5
4. Press ENTER
(Result is 144^.5 = 12)
FACTORIALS
EXAMPLE: Calculate 6!
1. Type 6
2. Press MATH
3. Move cursor onto option PRB
4. Move cursor onto option 4: !
5. Press ENTER
The screen shows 6!
6. Press ENTER
ANSWER: 6! = 720
NUMBER OF PERMUTATIONS nPr
EXAMPLE: Calculate 6P4 = 6 x 5 x 4 x 3 = 360
1. Type 6
2. Press MATH
3. Move cursor onto option PRB
4. Move cursor onto option 2: nPr
5. Press ENTER
The screen shows 6 nPr
6. Type 4
7. Press ENTER
ANSWER:
6P4 = 360
NUMBER OF COMBINATIONS nCr
EXAMPLE: Calculate 6C4 = 6!/[(6 - 4)! x 4!] = 15
1. TYPE 6
2. Press MATH
3. Move cursor onto option PRB
4. Move cursor onto option 3: nCr
5. Press ENTER
The screen shows 6 nCr
6. Type 4
7. Press ENTER
ANSWER:
6C4 = 15
CHAPTER 6
EXPECTED VALUE OF A DISCRETE RANDOM VARIABLE
Enter the values of X in column L1 of the STAT editor
Enter the probability values P(X) in column L2 of STAT editor
EXAMPLE: Insert the following values of X and P(X) into columns L1 and L2 of the STAT editor.
L1
L2
L3
2
.4
4
.3
6
.1
8
.2
We need to calculate X * P(X) and put these values in column L3
1. Move the cursor onto L3 at the top of column L3
2. Type 2ND L1 x 2ND L2
3. Press ENTER
Now the STAT editor looks like this:
L1
L2
L3
2
.4
0.8
4
.3
1.2
6
.1
0.6
8
.2
1.6
L4
L5
L6
The expected value of X is the sum of the values in column L3. To get the sum of the values in column L3,
proceed as follows:
1. Press STAT
2. Move cursor onto CALC
The screen highlights option 1: 1-Var Stats
3. Press ENTER
The screen shows “1-Var Stats”
4. Press 2ND L3
5. Press ENTER
(This tells the calculator to calculate descriptive statistics using the data in column L3)
The results show sumX = 4.2. That is, the sum of values in column L3 is E(X) = 4.2
CHAPTER 8:
FIND AREAS UNDER THE NORMAL DISTRIBUTION
THIS OPTION IS NOT AVAILABLE ON THE TI-82 CALCULATOR
EXAMPLE: Find the area between 90 and 115 under normal distribution with µ = 100 and σ = 15.
1. Press 2ND DISTR
(The “DISTR” option is above the “VARS” key)
2. Move cursor onto option 2: normalcdf(
3. Press ENTER
The screen shows normalcdf(
The general form is normalcdf(lower boundary, upper boundary, mean, standard deviation)
Thus, we need to input, the lower boundary, upper boundary, mean and standard deviation, all
separated by commas.
4. Type 90,115,100,15)
(You must type the commas; the closing parenthesis is optional)
5. Press ENTER
ANSWER: The area is .5888522734
SHORTCUT FOR THE STANDARD NORMAL DISTRIBUTION:
If µ = 0 and σ = 1, you do not need to enter these values. That is, N(0,1) is the default distribution.
EXAMPLE: Find the area between -1.96 and 1.96 under standard normal distribution.
1. Press 2ND DISTR
2. Move cursor onto option 2: normalcdf(
3. Press ENTER
The screen shows normalcdf(
4. Type -1.96,1.96)
(You must type the comma)
5. Press ENTER
ANSWER: The area is .9500043497
Compare with the answer in the textbook. The table in the book says that the area between 0 and
1.96 is .4750. Thus, the area between -1.96 and 1.96 is .9500. This is accurate to four decimal
places.
FIND AREA IN ONE TAIL OF THE NORMAL DISTRIBUTION
Suppose we want to find the area to the right of 2.00 under the standard normal distribution. One way to do
this is to find the area between 0 and 2.00 and subtract from .5000.
1. Press 2ND DISTR
2. Move cursor onto option 2: normalcdf(
3. Press ENTER
The screen shows normalcdf(
4. Type 0,2.00)
(You must type the comma)
(This calculates the area between 0 and 2.00)
5. Press ENTER
ANSWER: The area between 0 and 2.00 is .4772499375. Thus, the area to the right of 2.00 is
.0227500625
Compare with the answer in the textbook. The table in the book says that the area between 0 and 2.00 is
.4772. Thus, the area to the right of 2.00 is .0228. This is accurate to four decimal places.
ALTERNATIVE METHOD: FIND AREA IN ONE TAIL OF THE NORMAL DISTRIBUTION
Find the area to the right of 2.00 under the standard normal distribution.
1. Press 2ND DISTR
2. Move cursor onto option 2: normalcdf(
3. Press ENTER
For infinity, you need to press 2ND EE 99
(EE is above the comma key)
Similarly, for negative infinity, you would need to press -2ND EE 99
4. Type 2.00, 2ND EE 99)
(You must type the comma)
(This calculates the area between 2.00 and infinity)
5. Press ENTER
ANSWER: The area is .022750062
Compare with the answer in the textbook. The table in the book says that the area between 0 and
2.00 is .4772. Thus, the area to the right of 2.00 is .0228. This is accurate to four decimal places.
FIND THE VALUE OF X SUCH THAT THE AREA TO ITS LEFT IS A SPECIFIED AMOUNT
The general form is invNorm(desired area, mean, standard deviation)
Suppose we want to find the value of X such that the area to its left is, say, .975. Assume X is normal with µ
= 100 and σ = 15.
1. Press 2ND DISTR
2. Move cursor onto option 3: invNorm(
3. Press ENTER
The screen shows invNorm(
4. Type .975,100,15)
(You must type the commas)
5. Press ENTER
ANSWER: X = 129.3994598. The area between –infinity and 129.3994598 is .975.
CHAPTER 10
AREAS UNDER THE t-DISTRIBUTION
TI-82 DOES NOT HAVE THIS OPTION
EXAMPLE: Find the area between -1.23 and 1.833 under the t-distribution having 9 degrees of freedom.
1. Press 2ND DISTR
2. Move cursor onto option 5: tcdf(
3. Press ENTER
The screen shows tcdf(
The general form is tcdf(lower boundary, upper boundary, degrees of freedom).
Thus, we need to input, the lower boundary, upper boundary, and degrees of freedom, all separated
by commas.
4. Type -1.23,1.833,9)
(You must type the commas; the closing parenthesis is optional)
5. Press ENTER
ANSWER: The area is .8250518567
FIND AREA IN ONE TAIL OF THE t DISTRIBUTION
Usually, we want the area in the right hand tail of the t distribution.
EXAMPLE: Find the area to the right of 1.833 under the t-distribution having 9 degrees of freedom.
To find the area to the right of 1.833, we can find the area between 0 and 1.833 and subtract from .5000.
1. Press 2ND DISTR
2. Move cursor onto option 5: tcdf(
3. Press ENTER
The screen shows tcdf(
4. Type 0,1.833,9)
(You must type the commas; the closing parenthesis is optional)
5. Press ENTER
ANSWER: The area is .4499910308. Thus the area to the right of 1.833 is .0500089692.
Compare with the answer in the textbook. The table in the book says that, for 9 degrees of
freedom, the area to the right of 1.833 = .05. This is accurate to four decimal places.
ALTERNATIVE METHOD: FIND AREA IN ONE TAIL OF THE t DISTRIBUTION
EXAMPLE: Find the area to the right of 1.833 under the t-distribution having 9 degrees of freedom.
1. Press 2ND DISTR
2. Move cursor onto option 5: tcdf(
3. Press ENTER
The screen shows tcdf(
(EE is above the comma key)
(For infinity, you need to press 2ND EE 99
Similarly, for negative infinity, you would need to press -2ND EE 99
(You must type the commas; the closing parenthesis is optional)
4. Type 1.833,2ND EE 99,9)
(This calculates the area between 1.833 and infinity)
5. Press ENTER
ANSWER: The area is .0500089692
CHAPTER 10
FINDING A Z CONFIDENCE INTERVAL FOR THE MEAN
1. Enter the data in the STAT editor
Press STAT
The screen highlights EDIT
Press ENTER
Enter the X values in column L1
2. Calculate the sample mean. (We assume the population standard deviation is known.)
Press STAT
Move the cursor onto CALC
Press ENTER
The screen shows 1-Var Stats
Press ENTER
The screen shows the sample mean. Record the value of the sample mean for future use.
3. Press STAT
4. Move the cursor onto TESTS
5. Move the cursor onto option 7: ZInterval
6. Press ENTER
7. Move the cursor onto option Stats
8. Press ENTER
9. Move the cursor down to sigma and type the appropriate value of the standard deviation
10. Move the down to xbar and type the appropriate value
11. Move the cursor down to n: and type the sample size
12. Move the cursor down to C-Level and type the desired confidence level
13. Move the cursor down to Calculate and press ENTER
EXAMPLE:
Suppose xbar = 88; σ = 10; n = 50; level of confidence = 1 - α = .95
1. Press STAT
2. Move cursor onto TESTS
3. Move cursor onto 7: ZInterval
4. Press ENTER
5. Move cursor onto Stats
6. Press ENTER
7. Type the desired values for xbar, sigma, n, and C-Level
8. Move the cursor onto Calculate
9. Press ENTER
ANSWER: By hand calculation, the desired confidence interval is (85.22814142; 90.77185858).
My TI-83 calculator shows the result (85.228; 90.772)
CHAPTER 10
FINDING A t CONFIDENCE INTERVAL FOR THE MEAN
Follow the same procedure as that used for finding a z confidence interval for the mean except choose
option 8: TInterval rather than option 7: ZInterval. You will need to insert a value for the sample mean
and the sample standard deviation.
CHAPTER 10
FINDING A CONFIDENCE INTERVAL FOR THE POPULATION PROPORTION
Assume the sample size is 400. Assume the number of successes is X = 100. Calculate a 95% confidence
interval for the population proportion.
1. Press STAT
2. Move cursor onto TESTS
3. Move cursor down onto A: 1-PropZInt
4. Press ENTER
5. Type in the appropriate values for X, n, and C-Level (confidence level)
6. Move the cursor onto Calculate
7. Press ENTER
ANSWER: The screen shows (.20757; .29243); phat = .25; n = 400
CHAPTER 11
HYPOTHESIS TEST FOR THE MEAN (Z-TEST)
Test the null hypothesis H0:µ = 100 against the one-sided alternative H1: µ > 100. Assume the population
standard deviation is σ = 15. Assume the sample mean is 104 and n = 64.
1. Press STAT
2. Move cursor onto TESTS
The cursor will highlight option 1: Z-Test
3. Press ENTER
4. Move cursor onto Stats
5. Press ENTER
6. Type in the appropriate values for the hypothesized mean, the population standard deviation, the sample
mean, and the sample size
7. Move the cursor onto the desired test (two-sided or sone-sided)
8. Press ENTER
9. Move the cursor onto option Calculate
10. Press ENTER
ANSWER: The screen shows the observed value of z = 2.13333 and the p-value of the test is p =
.0164486368. If we had chosen to use a 2.5% level of significance, the critical value of z would be z
= 1.96. Since the observed value of z exceeds the critical value, it falls in the critical region, and we
would reject the null hypothesis. Alternatively, since the p-value of the test is less than the level of
significance, we would reject the null hypothesis.
CHAPTER 11
HYPOTHESIS TEST FOR THE MEAN (t-TEST)
Test the null hypothesis H0:µ = 90 against the one-sided alternative H1:µ > 90. Assume the sample
standard deviation is Sx = 16. Assume the sample mean is 94 and n = 25.
1. Press STAT
2. Move cursor onto TESTS
Move the cursor onto option 2: T-Test
3. Press ENTER
4. Move cursor onto Stats
5. Press ENTER
6. Type in the appropriate values for the hypothesized mean, the sample standard deviation, the sample
mean, and the sample size
7. Move the cursor onto the desired test (two-sided or one-sided)
8. Press ENTER
9. Move the cursor onto option Calculate
10. Press ENTER
ANSWER: The screen shows the observed value of t = 1.25 and the p-value of the test is p =
.1116757391. If we had chosen to use a 2.5% level of significance, the critical value of t (with 24
degrees of freedom) for a one-tailed test would be t = 2.064. Since the observed value of t is less
than the critical value, it falls in the acceptance region, and we would not reject the null hypothesis.
Alternatively, since the p-value of the test is greater than the level of significance, we would not
reject the null hypothesis.
CHAPTER 11
HYPOTHESIS TEST FOR THE POPULATION PROPORTION
Test the null hypothesis that H0:p = .60 against the one-sided alternative H1:p < .60. Assume the sample
size is n = 400 and X = 220. Assume the desired level of significance is α = 1%.
1. Press STAT
2. Move cursor onto TESTS
The cursor will highlight option 5: 1-PropZ-Test
3. Press ENTER
4. Move cursor onto Stats
5. Press ENTER
6. Type in the appropriate values for the hypothesized population proportion, X and n.
7. Move the cursor onto the desired test (two-sided or sone-sided)
8. Press ENTER
9. Move the cursor onto option Calculate
10. Press ENTER
ANSWER: The screen shows the observed value of z = -2.041241452 and the p-value of the test is
p = .0206133484. We chose a 1.0% level of significance, so the critical value of z would be z = -2.33. Since
the observed value of z exceeds the critical value, it falls in the acceptance region, and we would not reject
the null hypothesis. Alternatively, since the p-value of the test is greater than the level of significance, we
would not reject the null hypothesis.
CHAPTER 15
LINEAR REGRESSION AND CORRELATION
You need to know which variable is the dependent variable (Y) and which is the independent variable (X).
The default option is to put X in column L1 and Y in column L2 in the STAT editor.
Calculate the regression equation using the following data, where X is in L1 and Y is in L2:
L1
L2
2
7
4
13
6
22
8
26
1.
2.
3.
4.
Press STAT
Move cursor onto CALC
Move cursor onto option 4: LinReg(ax+b)
Press ENTER
The screen shows LinReg(ax+b)
(Because we have X in L1 and Y in L2, we do not need to specify the column locations for X and Y)
NOTE: Alternatively, you can use option 8: LinReg(a+bx)
You will get the exact same values, but now a is the intercept and b is the slope.
5. Press ENTER
ANSWER: The screen shows the following results:
a = slope = 3.3
b = intercept = .5
r = correlation coefficient = .9904953716
r2 = .9810810811
Thus, the estimated regression equation is: Y = 3.3X + .5
FOOTNOTE: What if, say, X is in column L4 and Y is in column L3?
1. Press STAT
2. Move cursor onto CALC
3. Move cursor onto option 4: LinReg(ax+b)
4. Press ENTER
The screen shows LinReg(ax+b)
(Because we have X in L4 and Y in L3, we do need to specify the column locations for X and Y)
5. Press 2ND L4, 2ND L3
(The first location is always the X variable; you must type the comma, the 2nd location is the Y variable.)
6. Press ENTER
CORRELATION COEFFICIENT: TI-83 ONLY
If your calculator does not show the correlation coefficient along with the regression results, proceed as
follows.
1. Press 2ND CATALOG (Option “CATALOG” is above the "0" key)
2. Move the cursor down until it points at option DiagnosticOn
3. Press ENTER TWICE
In the future, the calculator will always show the correlation coefficient along with the estimated slope and
intercept.
CHAPTER 15
TESTING THE HYPOTHESIS THAT THE CORRELATION COEFFICENT IS ZERO
1.
2.
3.
4.
5.
6.
7.
8.
Press STAT
Move the cursor onto TESTS
Move the cursor onto E: LinRegTest
Press ENTER
Make sure Xlist shows L1 (for variable X) and Ylist shows L2 (for variable Y)
Move the cursor onto the appropriate alternative hypothesis
Press ENTER
Move the cursor onto Calculate and press ENTER
ANSWER: The screen shows the observed value of t = 10.1840211 with 2 degrees of freedom.
You must choose an appropriate level of significance and find the critical value of t using the tdistribution table. Compare the observed value of t with the critical value of t and make the
appropriate decision. Also, the screen shows that the p-value of the test is .0047523142. Reject
the null hypothesis if the p-value is less than the level of significance.
CHAPTER 15
TO GRAPH A SCATTERPLOT
1. Enter the X values in column L1 and the Y values in column L2
2. Press WINDOW
(The WINDOW key is at the top of the keyboard.)
3. Make sure the WINDOW values are appropriate for your X and Y data. Type an Xmin value which is
slightly less than the smallest X value and an Xmax value which is slightly larger than the largest X value.
Do the same for Ymin and Ymax. In general, the values Xscl, Yscl and Xres can be set equal to 1.
2. Press 2ND STAT PLOT
(Option STAT PLOT is above the “Y=” key at the top left of the keyboard.)
3. Option 1: Plot 1 will be highlighted
Press ENTER
4. A new screen appears
Put the cursor on option “On”
Press ENTER
5. Move the cursor down to Option Type
Move the cursor over onto the first graph symbol (which looks like a scatterplot).
. Press ENTER
6. Make sure Xlist shows L1 and Ylist shows L2
(provided X is in L1 and Y is in L2)
For Mark, highlight the square symbol, the “+” symbol, or the period symbol, to mark your data points
6. Press GRAPH
(The “GRAPH” key is located on the top right of the keyboard.)
The scatterplot will now appear. If you do not like its appearance, change the WINDOW settings or the
STAT PLOT choices.
CHAPTER 15
TO PLOT A REGRESSION LINE ON THE SCATTERPLOT
1. Use the STAT editor and calculate the equation of the sample regression line
2. Press Y=
(The “Y=” key is located at the top left of the keyboard.
3. If necessary, press CLEAR to clear any previous equation listed at equation Y1
4. Press VARS
5. Move cursor onto option 5: Statistics
6. Press ENTER
7. Move cursor onto option EQ
(Highlight option 1: RegEq)
8. Press ENTER
(The screen shows the regression equation next to equation Y1.)
9. Press GRAPH
(The screen should show the regression line superimposed onto the scatterplot.)
CHAPTER 15: (OPTIONAL)
CALCULATE VALUES OF Y, THE PREDICTED VALUES OF Y
In the last example, X and Y were in columns L1 and L2, and the estimated regression equation was
Y = 3.3X + .5
Alternatively, this could be expressed as
Y = .5 + 3.3X
Let us calculate the predicted values of Y
and put these values in column L3.
(Y = 3.3X + .5)
1. Press STAT
Cursor highlights EDIT
2. Press ENTER
3. Move the cursor onto L3 at the top of column L3
4. Type 3.3 x 2ND L1 + .5
This tells the calculator to multiply the values in L1 by 3.3 and then add .5
5. Press ENTER
The predicted values appear in column L3.
X
L1
2
4
6
8
Y
L2
7
13
22
26
Y
L3
7.1
13.7
20.3
26.9
CHAPTER 15: (OPTIONAL)
CALCULATE THE RESIDUALS
The residuals are equal to
ê=Y-Y
The values of Y and Y are in columns L2 and L3.
Let us put the residuals in column L4.
1. Press STAT
Cursor highlights EDIT
2. Press ENTER
3. Move the cursor onto L4 at the top of column L4
4. Type 2ND L2 – 2ND L3
5. Press ENTER
The residuals appear in column L4
X
L1
2
4
6
8
Y
L2
7
13
22
26
Y
L3
7.1
13.7
20.3
26.9
ê
L4
-.1
-.7
1.7
-.9
As a check, calculate the sum of the values in column L4.
(Observe that the residuals sum to zero.)
CHAPTER 15: (OPTIONAL)
CALCULATE SSE: THE SUM OF SQUARED RESIDUALS
SSE = Sum of squared residuals
The Residuals are in column L4
Let us square each residual and place them in column L5.
1. Press STAT
Cursor highlights EDIT
2. Press ENTER
3. Move the cursor onto L5 at the top of column L5
4. Type 2ND L4 x 2ND L4
This tells the calculator to square each value in L4 and store the squares in L5
5. Press ENTER
The squared residuals appear in column L5 as shown below
X
L1
2
4
6
8
Y
L2
7
13
22
26
Y
L3
7.1
13.7
20.3
26.9
ê
L4
-.1
-.7
1.7
-.9
ê*ê
L5
0.01
0.49
2.89
0.81
L6
SSE is the sum of the values in column L5. To get this sum, proceed as follows:
1. Press STAT
Cursor highlights EDIT
2. Move cursor onto CALC
Cursor highlights 1: 1-Var Stats
4. Press ENTER
The screen shows 1-Var Stats
5. Type 2ND L5 (To get descriptive statistics results using data from column L5)
The results appear
The sum of the values in column L5 is SSE = 4.2
FASTEST WAY TO CLEAR ALL DATA FROM STAT EDITOR
1. Press 2ND MEM
2. Move cursor onto option 4: ClrAllLists
3. Press ENTER
TO STORE A VALUE IN A MEMORY
Often it is useful to store a value in a calculator memory, so it can be recalled later in a problem.
EXAMPLE: Store the value 800 in memory Y. (For example, memory Y is above the "1" key, memory Z is
above the "2" key, etc.)
1. Type the value 800
2. Press STO
3. Press ALPHA
(This tells the calculator that you want to choose a memory indicated by a letter
shown above a key)
4. Press Y (The “Y” is above the number “1” key)
The value 800 is now stored in memory Y
5. Press ENTER
In short, here's how to store the value 800 in memory Y.
1. Type 800
2. Press STO
3. Press ALPHA
4. Press Y
5. Press ENTER
TO RECALL A VALUE FROM A MEMORY
1. Press 2ND RCL
(RCL is above the STO key)
2. Press ALPHA Y
This will recall the value 800 from memory Y
3. Press ENTER
STORING VALUES IN MEMORY ON TI-82
PUT 10 IN MEMORY T, 15 IN MEMORY U, 20 IN MEMORY V
1. 10 STO ALPHA T ENTER
2. 15 STO ALPHA U ENTER
3. 20 STO ALPHA V ENTER
USING VALUES STORED IN MEMORY
ADD 10 + 15 + 20
1. ALPHA T + ALPHA U + ALPHA V ENTER (RESULT IS 45)
DIVIDE 20 BY 10
2. ALPHA V / ALPHA T ENTER (RESULT IS 2)
Now we are ready to calculate the values of Yhat.
Let us put the values of Yhat in L3.
1. Press STAT
2. Move arrow to EDIT
3. Press ENTER
4. Move arrow to TOP of L3 (above the line)
5. Press 2ND Y-VARS
A new menu appears with Function highlighted
6. Press ENTER
A new menu appears with Y1 highlighted
7. Press ENTER
The data list screen appears. At the bottom, the screen says, L3 = Y1
8. Press ( 2ND L1 ) ENTER , i.e (2nd L1) (you need the parentheses)
The predicted values are now in L3
TO CLEAR SELECTED MEMORIES AND DATA LISTS
1. 2ND MEM
Screen shows a new menu
2. Select DELETE
SCREEN SHOWS A NEW MENU
3. SELECT ALL
Screen shows a all memories and lists that are in use
3. Move arrow to any item and Press ENTER
THAT ITEM IS DELETED
4. TO EXIT, 2ND QUIT
TO RENAME THE COLUMN HEADINGS IN THE STAT EDITOR
If, you renamed some of the columns in the STAT editor, you probably want to get back to the standard L1,
L2, L3, numbering. Here's how to do it.
1. Press STAT
The screen highlights EDIT
2. Move the cursor onto option 5: SetUpEditor
3. Press ENTER