Calculator Tips and Tricks

 

Listed below are some useful TI-83/84 graphing calculator commands for Stats 60. It is not necessary to know these commands for the homeworks and exams, but they may be helpful for checking your work.

General Tip: To access any of the menus in yellow above each button, press 2ND (the yellow button at the top left) and then the corresponding button.

(Click the calculator to enlarge.)

Mean and SD of a List of Numbers

  1. Enter the data into a list.

    1. Press STAT and select EDIT > 1:Edit…

    2. Enter the data into L1 (or any other list), one entry per line.

    3. To clear list L1, make sure the cursor is over the L1, press CLEAR and ENTER.

  2. Press STAT and select CALC > 1:1-Var Stats

  3. Now type in the symbol L1 (either press 2ND + 1, or go to LIST (2ND + STAT) and select L1 from the NAMES menu) and press ENTER.

  4. The mean is bar x, the SD is sigma_X. (Note: the SD+ is s_X and if you scroll down you can also find the median and the quartiles.)

Correlation and Regression Line

  1. Enter the X data into L1 and the Y data into L2. (See above for how to do this.)

  2. Press STAT and select CALC > 4:LinReg(ax+b)

  3. Now type in the symbol L1, followed by ,, then the symbol L2.

  4. You should see the slope and intercept of the regression line, followed by r and r-squared. If you do not see r and r-squared, you need to set DiagnosticOn. To do this, go to CATALOG (2ND + 0), scroll down until you see DiagnosticOn, and press ENTER.

Caution

The value of r — and hence the slope and intercept — will be different from what you would get using the formulas in the book. The reason is that the calculator uses the more conventional formula for r where you divide by (n-1) instead of n:

  	r = frac{1}{n-1} sum_{i=1}^n left( frac{X_i - bar X}{SD(X)} right) left( frac{Y_i - bar Y}{SD(Y)} right)

To convert the r on the calculator to the r in the book, multiply by (n-1)/n.

Normal Distribution

Area under Normal Curves

  1. Go to DISTR (2ND + VARS) and select DISTR > 2:normalcdf(

  2. You can use this function in one of two ways:

    1. If you enter normalcdf(a,b), it will give you the area between a and b SD's from the mean. (Check that when a=-1 and b=1, the calculator returns 68%!)

    2. If you enter normalcdf(a,b,avg,SD), it will give you the area between a and b for a normal curve with the given average and SD.

    3. Tip: To find the area less than b, set a to some ridiculously low number, i.e. -999.

Note

You are expected to learn to use normal tables for this course. Although the calculator can give more precise areas than the table, you should give the answer you would get from a table and use the calculator output only as a check.

Percentiles of Normal Curves

  1. Go to DISTR (2ND + VARS) and select DISTR > 3:invNorm(

  2. You can use this function in one of two ways:

    1. If you enter invNorm(p), it will give you the pth percentile for a standard (mean 0 and SD 1) normal curve. (i.e. invNorm(.975)approx2).

    2. If you enter invNorm(p,avg,SD), it will give you the pth percentile for a normal curve with that mean and SD (i.e. invNorm(.5,3,1)=3).

Binomial Coefficients and Probabilities

To calculate a binomial coefficient {n choose k} = frac{n!}{k!(n-k)!}, you need the nCr symbol. To retrieve this symbol, press MATH and select PRB > 3:nCr. To calculate {5 choose 3}, type 5 nCr 3 and press ENTER.

If your ultimate goal is to calculate a binomial probability, there is an easier way than calculating {n choose k} p^k (1-p)^{n-k} manually. Go to DISTR (2ND + VARS) and select 0:binompdf(. binompdf(n,p,k) gives the probability of k successes in n trials when the success probability is p.

There is also the option binomcdf(n,p,k), which gives the probability of leq k successes.

Note

Although binomcdf allows you to obtain exact probabilities for situations where we'd ordinarily use a normal approximation, you should still use the normal approximation on homeworks and exams and use binomcdf only as a check.

Hypothesis Tests

All of the following tests can be found under TESTS. To get to TESTS, press STAT and the right arrow twice.

z-test for means

  1. Go to 1:Z-Test.

  2. Make sure the input is set to Stats, not Data (since you will usually not be dealing with the raw data).

  3. Enter the data for computing the test statistic.

    1. mu_0 is the hypothesized mean under the null.

    2. sigma is the SD of the box. (Enter the SD of the sample if SD(box) is unknown.)

    3. bar x is the observed average of the sample.

    4. n is the sample size.

  4. Specify the alternative hypothesis: i.e. is the average of the box <mu_0 or >mu_0 (the two most common scenarios in this class)?

  5. Select Calculate to see the results of the test, or Draw if you want to see the normal curve with the p-value shaded.

z-test for proportions

  1. Go to 5:1-PropZTest

  2. Enter the data for computing the test statistic.

    1. p_0 is the hypothesized proportion under the null.

    2. x is the observed number of successes.

    3. n is the sample size.

  3. Specify the alternative hypothesis: i.e. is the proportion of ones <p_0 or > p_0 (the two most common scenarios in this class)?

  4. Select Calculate to see the results of the test, or Draw if you want to see the normal curve with the p-value shaded.

t-test

  1. Go to 2:T-Test

  2. Make sure the input is set to Stats, not Data (since you will usually not be dealing with the raw data).

  3. Enter the data for computing the test statistic.

    1. mu_0 is the hypothesized mean under the null.

    2. bar x is the observed average of the sample.

    3. s_X is the SD+ of the sample.

    4. n is the sample size.

  4. Specify the alternative hypothesis: i.e. is the average of the box <mu_0 or >mu_0 (the two most common scenarios in this class)?

  5. Select Calculate to see the results of the test, or Draw if you want to see the t curve with the p-value shaded.

2-Sample z-test for means

  1. Go to 3:2-SampZTest

  2. Make sure the input is set to Stats, not Data (since you will usually not be dealing with the raw data).

  3. Enter the data for computing the test statistic.

    1. sigma_1 and sigma_2 are the SD of the two boxes. (Enter the SD's of sample 1 and sample 2 if the SD's of the boxes are unknown.)

    2. bar x_1 and bar x_2 are the observed means of the two samples.

    3. n_1 and n_2 are the sizes of the two samples.

  4. Specify the alternative hypothesis: i.e. is the average of box 1 > or < the average of box 2?

  5. Select Calculate to see the results of the test, or Draw if you want to see the normal curve with the p-value shaded.

2-Sample z-test for proportions

  1. Go to 6:2-PropZTest

  2. Enter the data for computing the test statistic.

    1. n_1 and n_2 are the size of samples 1 and 2 (e.g. the number of people surveyed).

    2. x_1 and x_2 are the number of successes in samples 1 and 2.

  3. Specify the alternative hypothesis: i.e. is the proportion of ones in box 1 (p_1) > or < the proportion of ones in box 2 (p_2)?

  4. Select Calculate to see the results of the test, or Draw if you want to see the normal curve with the p-value shaded.

Caution

The calculator calculates the SD of the difference of two proportions in a slightly different way than the textbook, so you will get a slightly different answer if you follow the formula in the book.

Chi-Square Test for Independence

Note

The following describes how to perform a chi-square test of whether two categorical variables are independent. It cannot be used to test whether a categorical variable fits some distribution (a ‘‘goodness-of-fit’’ test). In other words, if you are trying to perform a chi-square test on a one dimensional table, you're out of luck. On some newer calculators, there is also an option D:chi^2GOF-Test. I don't have it on mine, so if you want to try that out, you're on your own.

  1. You will first need to enter the observed counts into a matrix (i.e. a table):

    1. Go to MATRIX (2ND + x^{-1}) and select EDIT > the matrix you want to edit (let's say [A]).

    2. Enter the dimension of the matrix: (# rows x # cols).

    3. Enter the counts into the matrix.

    4. Exit by pressing 2ND + MODE (i.e. QUIT).

  2. Go to C:chi^2-Test.

  3. Make sure [A] is selected as the Observed matrix. (If it's not, go to MATRIX and select NAMES > 1: [A].)

  4. Select Calculate to see the results of the test, or Draw if you want to see the chi-square curve with the p-value shaded