GETTING BACK TO THE MAIN WINDOW (HOME SCREEN)
Press 2nd, QUIT.
REPEATING THE LAST ENTRY Press 2nd, ENTRY. You then can edit the entry and press ENTER to do the new calculation. You can repeat the 2nd, ENTRY keys to go back several entries.
TURNING OFF A FUNCTION If you wish to take a function out of a graph but you don’t want to delete the function, press Y= and put the cursor on the equals sign ( = ) for that function. Then press ENTER. To turn the function back on, do the same steps.
There are lots of other tricks. I find new ones every semester!
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STEP 1 PUT THE DATA IN A LIST.
The first step in any statistical work is to put the data into the calculator. You cannot do anything without data!
Press the buttons STAT, EDIT. There are six lists you can use, numbered from L1 to L6. Put each set of data into its own list.
If you wish to sort the data into ascending order (smallest to largest), you can use the commands STAT, SortA, ENTER. Then specify which list to sort (for instance, 2nd, L1) and press ENTER. This can also be done for descending order by using SortD.
STEP 2 MAKING A HISTOGRAM
Get to the Statistical Plots menu by pressing 2nd, STAT PLOT. Then choose one of the plots and press ENTER. There can be up to three plots simultaneously, though we will usually use only one at a time. Set the plot commands to:
On, the 3rd type (with the bars), L1 (or whatever list holds your data).
Leave the Frequency set at 1.
Now set a viewing window that shows your histogram. To do so, use ZOOM, ZoomStat. This automatically picks a window that holds the entire graph. It may not be the best choice for this window, however. To adjust the window, press WINDOW and change the values of Xmin, Xmax, Ymin, Ymax.
An important value is Xscl which tells how wide to make each bar in the histogram. Changing the width of the bars can drastically affect how the graph looks.
Once the graph has been drawn, the TRACE key and the arrow keys will give you information about the graph.
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STEP 1 PUT THE DATA IN A LIST.
Reminder: If you wish to sort the data into ascending order (smallest to largest), you can use the commands STAT, SortA, ENTER. Then specify which list to sort (for instance, 2nd, L1) and press ENTER. This can also be done for descending order by using SortD.
STEP 2
Press STAT, CALC, 1-VAR STATS, ENTER. Then tell which list of data to use. For example, you might use 2nd, L1, ENTER. These commands will produce a list of results.
In MATH 205 we will pay attention to:
"x bar" = the mean
Sx = the standard deviation
n = the number of data items
minX = the smallest data value
Q1 = the first quartile
Med = the median
Q3 = the third quartile
maxX = the largest data value
(Later we will use the 2-VAR STATS and the LinReg commands also.)
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STEP 1 PUT THE DATA IN A LIST.
STEP 2
This is exactly like making a histogram except that the type of StatPlot is different. For the type, pick the fifth option (in the middle of the second row) to get a simple boxplot. Or pick the fourth option to get a boxplot that shows any outliers.
TRACE is useful for boxplots too.
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The goal is to find the percentage of the data in the distribution that lies between two values, which we can call the lower boundary and the upper boundary. In addition, we need to know the mean and the standard deviation for the particular normal distribution.
Use the commands 2nd, Distr, normalcdf, Enter. Then tell the lower boundary, the upper boundary, the mean, and the standard deviation, then press Enter.
For example, the percentage of data between 100 and 150 for the normal distribution N(125, 45) – which equals the area under this normal curve and between these two boundaries – is calculated by normalcdf(100, 150, 125, 45).
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STEP 1 PUT THE DATA IN TWO LISTS. Make sure that the pairs of values are together. For instance, if the numbers 73 and 205 belong in a pair, they should be in the same position for both lists. So the lists have to stay in the same order.
STEP 2 Get to the Statistical Plots menu by pressing 2nd, STAT PLOT. Then choose one of the plots and press ENTER. Set the plot commands to:
On, with the 1st type (with the axes and the dots).
Tell which two lists hold your data.
Now set a viewing window that shows your histogram. To do so, use ZOOM, ZoomStat. This automatically picks a window that holds the entire graph. It may not be the best choice for this window, however. To adjust the window, press WINDOW and change the values of Xmin, Xmax, Ymin, Ymax.
Once the graph has been drawn, the TRACE key and the arrow keys will give you information about the graph. The cursor will move through the points in the order in which they appear in the data list.
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STEP 1 Put the data in two lists, just like you did to make a scatterplot. Make sure that the lists in the corresponding order.
STEP 2 Press STAT, CALC, LinReg (either one), then ENTER. Tell which two lists of data to use, then press ENTER.
For example, LinReg L3, L4 will calculate the r value for the data in lists L3 and L4. (Other things are calculated too, which are discussed below.)
If the r value does not appear when you do this, you must turn on the Diagnostics mode. Press 2nd, CATALOG then scroll down to DiagnosticOn and press ENTER, ENTER. Then try the correlation calculation again. Once it is turned on, you should never have to do this Diagnostic command again.
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STEP 1 Put the data in two lists, in the corresponding order. You can create the scatterplot now or later.
STEP 2 To calculate the regression line, do the same commands as when calculating the correlation value. So press STAT, CALC, LinReg (either one), then ENTER. Tell which two lists of data to use, then press ENTER.
STEP 3 To plot this line, press Y= then put the cursor on one of the functions. You must find the equation and put it into this function. To do so, press VARS, Statistics, EQ, RegEq, ENTER. Now create the scatterplot. The line should appear in the graph.
STEP 4 To find a y-value along the regression line, press VARS, Y-VARS, Function, choose the correct function, ENTER, (, type your x-value, ), ENTER.
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STEP 1 Put the data into two lists and do the LinReg calculation.
STEP 2 During the LinReg calculation the calculator automatically calculates the residuals. You must put the results into a list. Press LIST, NAMES, RESID, STO® , tell which list to use (usually you want a new list), then ENTER.
STEP 3 Now create a scatterplot, using the same Xlist as the previous scatterplot and using the residual list as the Ylist.
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MAKING A HISTOGRAM Put the possible outcomes (i.e. the sample space) in a list. In another list put the frequencies. Make sure that the lists are in the corresponding order. Then create a histogram in the usual way; however, under Freq tell which list contains the frequencies.
You can use relative frequencies (percentages) if you wish.
FINDING MEAN AND STANDARD DEVIATION FOR A PROBABILITY DISTRIBUTION Put the outcomes and their frequencies in two lists, in the corresponding order. Press STAT, CALC, 1-Var Stats, then ENTER. Tell which list has the values, then which list has the frequencies, then press ENTER.
For example, 1-Var Stats L3, L4 will calculate for the outcomes in list L3 with frequencies in list L4.
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CALCULATING A BINOMIAL PROBABILITY From the Home Screen, do 2nd, DISTR, then arrow down to binompdf( , and press ENTER. Now you need to tell the number of trials n, the probability of success p, and the desired number of successes. For example, the command binompdf( 5, 0.75, 2 ) asks for the probability of getting two Heads in five tosses of an unbalanced coin that comes up Heads 75% of the time.
There is also the command binomcdf, which is the cumulative binomial calculation. (Don’t confuse the two commands!) The command binomcdf( 5, 0.75, 2 ) calculates the total probability of getting 0, 1, or 2 successes in the five trials. So if we wanted the probability of getting more than two Heads in five tosses of this unbalanced coin, we could do 1 - binomcdf( 5, 0.75, 2 )
(These commands do not seem to work when n is very large, like 1000. In that situation you must do a normal approximation to the binomial distribution.)
DRAWING A BINOMIAL DISTRIBUTION This will be a histogram using binomial probabilities as the frequencies. Put the possible values in one list. For example, if we are tossing a fair coin five times, put 0, 1, 2, 3, 4, 5 into list L1. Put the cursor at the very top of the L2 column, highlighting the L2. Then do the command binompdf(4,0.5,L1) and press ENTER. The calculator will fill in the values for the probabilities.
Next create a histogram using L1 as the X values and L2 as the frequencies. You will need to adjust the window to get a good graph, and you should use Xscl = 1.
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Press the Y= button and put the cursor on one of the functions. Then do 2nd, DISTR and select normalpdf. You must then tell the variable X, the mean, and the standard deviation for the distribution. For example, Y1 = normalpdf( X, 74, 22 ) will graph the normal distribution having a mean of 74 and a standard deviation of 22.
You will have to adjust the window. Recall the 68-95-99.7% Rule; if you choose an Xmin three standard deviations below the mean and choose an Xmax three standard deviations above the mean, you will have the entire curve (almost ). You will have to experiment with the minimum and maximum Y-values to get a good graph. I suggest thinking small, such as Ymin = -0.1 and Ymax = 0.5 to start with.
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There are many of these available by pressing STAT, TESTS.
ZInterval This command calculates a confidence interval estimate for a mean by using a normal distribution. You must know the population parameter s to use this.
Z-Test This command tests hypotheses by using a normal distribution. The test can be based on a list of data or on statistics you provide. You must know the value of s to use this. You have the option of getting just the calculated results or getting a picture of the distribution with the appropriate region marked.
TInterval This command calculates a confidence interval estimate for a mean by using a t-distribution. You do not need to know anything about the population.
T-Test This command tests hypotheses by using a t-distribution. The test can be based on a list of data or on statistics you provide. You have the option of getting just the calculated results or getting a picture of the distribution.
Later in the semester we will use more of these procedures.
1-PropZInterval This command finds a confidence interval for a proportion of a population. It uses statistics from one sample and is based on a normal distribution. (Note that the Wilson estimate requires some adjustments to this procedure.)
1-PropZTest This command is a hypothesis test for a proportion of a population. It uses statistics from one sample and is based on a normal distribution. (Again, the Wilson estimate requires some adjustments to this procedure.)
2-SampTInterval This procedure estimates the difference between two population means. It uses data or statistics from two samples and is based on a t-distribution.
2-SampTTest This command is a hypothesis test for comparing the means of two populations. It uses data or statistics from two samples and is based on a t-distribution.
2-PropZInterval This procedure estimates the difference between two population proportions. It uses statistics from two samples and is based on a normal distribution.
2-PropZTest This command is a hypothesis test for comparing the proportions of two populations. It uses statistics from two samples and is based on a normal distribution.
Chi Squared-Test This command is a hypothesis test for comparing two categorical variables. First the observed data must be put into a matrix. Again, there is the option of getting just the calculated results or getting a picture of the Chi Squared-distribution.
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Chi Squared-Tests with the TI-83
PUT THE OBSERVED COUNTS INTO A MATRIX For our purposes, a matrix is just a grid of numbers. Press MATRX, EDIT, then select one of the matrices and press ENTER. Make sure it has the correct number of rows and columns for your data, then put in the values of the observed counts.
RUN THE TEST Press STAT, TESTS, then find Chi Squared-Test and press ENTER. Then tell which matrix has the observed counts and which matrix should hold the expected counts. (You can use the default entries or change them. To make a change, put the cursor on that spot, then press MATRX and select the matrix you want.) After everything is correct, select Calculate or Draw then press ENTER.
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