Using the TI-83 Statistical Features

Transcription

1 Entering data (working with lists) Consider the following small data sets: Using the TI-83 Statistical Features Data Set 1: {1, 2, 3, 4, 5} Data Set 2: {2, 3, 4, 4, 6} Press STAT to access the statistics menu. The default setting, EDIT 1:Edit... is highlighted. Press ENTER to create or change any one of the six built-in lists. Here s what comes up after you press ENTER. Enter Data Set 1 in L 1 by typing each number followed by ENTER. The function-like notation L1(6) in the lower left corner indicates the 6 th data value in the list. When you are finished your screen should look like this. To move to list L 2 press the right arrow key. Now enter Data Set 2. Clearing Old Data (quick way) Use the key to highlight the name of the list. Press CLEAR and then ENTER or. Working with the Data Press STAT to highlight the CALCulations menu. 1

2 STAT CALC menu 1: 1-Var Stats Calculates descriptive statistics for data with one measured variable. 4: LinReg(ax+b) For two-variable data (ordered pairs), calculates a linear regression or equation. There are two forms to choose from 4:y=ax+b or 8:y=a+bx. 8: LinReg(a+bx) When DiagnosticOn (in the catalog menu) is set, r and r 2 are also displayed. Let s look at both of these: 1-Var Stats: If you have one-variable data (one set of numbers) we can calculate summary statistics by accessing the default 1:1-Var Stats. Pressing ENTER will copy this command to the home screen. Now you need to tell the calculator the name of the list that contains your data. Press 2 nd L1 (above the 1 key). Your screen should look like this: Now, press ENTER again to perform the 1-Variable calculations using the data from list L 1. Here s a list of what is displayed. : mean (sample or population) Σx : sum of the data values Σx 2 : sum of squares (square each number, then add) s x : sample standard deviation σ x : population standard deviation n : number of values in the data set The arrow in the lower left corner of the screen indicates that there is more. Press 5 times to see what s left MinX : the lowest value in the data set Q1 : first quartile (25% of the data is less than or equal to this value) Med : median (50% of the data is less than or equal to this value) Q3 : third quartile (75% of the data is less than or equal to this value) maxx : the highest value in the data set For practice, repeat the process for list L 2. Here are the two screens you should see after performing the 1-Variable calculations. 2

3 Linear Regression If you have two-variable data (ordered pairs) we can calculate the linear regression equation, correlation coefficient (r), and coefficient of determination (r 2 ) by accessing either 4:LinReg(ax+b) or 8:LinReg(a+bx). Pressing 4 or 8 will copy this command to the home screen. Now you need to tell the calculator the name of the lists that contains your data. Press 2 nd L1 (above the 1 key) for the location of the x data, press, and 2 nd L2 (above the 2 key) for the location of the y data.. Your screen should look like this: Now, press ENTER again to perform the Linear Regression calculations using the data from list L 1 and L 2. Plotting the Data Next we will take a look at the six data graphs available on the TI-83 (scatter plot, xyline, histogram, modified box plot, box plot, normal probability plot). To access the plots, press 2 nd STAT PLOT (above Y=). Here is the screen you should see. You may work with three different plots from up to three data sets at a time. Here s a summary of the different types of plots you will probably use. Histogram Plots one variable data. Xscl determines the width of each bar, beginning at Xmin. A value that occurs on the edge of a bar is counted in the bar to the right. Boxplot Plots one variable data. The whiskers extend from the minimum data value to the first quartile (Q 1 ) and from the third quartile (Q 3 ) to the maximum data value. The box is defined by Q 1, median (Med), and Q 3. Box plots are plotted with respect to Xmin and Xmax and ignore Ymin and Ymax. 3

4 Scatter Plots two variable data. Use ZoomStat (Zoom #9) to adjust Xmin, Xmax, Ymin, and Ymax automatically. Let s look at an example of each. Histogram: Use the data in L 2. From the STAT PLOT menu press ENTER to access Plot 1. Use the arrows to move the cursor around to either turn this graph ON or OFF and select the graph type. Xlist is where we name the list containing the data on the horizontal axis. Freq is 1 (to count each number in the Xlist one time) or the name of another list which contains the frequencies. Press WINDOW to setup the intervals the graph will use. Xmin is where the first interval begins. The width of each interval is determined by Xscl. Ymax must be larger than the highest frequency of any interval. Press GRAPH to view the plot. Press TRACE and see what happens! Boxplot: Use the data in L 1. From the STAT PLOT menu press 2 to access Plot 2. Xlist is where we name the list containing the data. Freq is 1 (to count each number in the Xlist one time) or the name of another list which contains the frequencies. You can either use WINDOW to setup the window or press ZOOM 9:ZoomStat to adjust the window automatically. Be sure to turn Plot 1 OFF first. Press GRAPH to view the plot. Press TRACE and see what happens! Scatter: Use the data in L 1 to represent the x variable data and L 2 to represent the y variable data. Xlist is the name of the list containing the data represented on the x axis and Ylist is the name of the list containing the data represented on the y axis. Mark represents the symbol that will be used to show the position of the dots (ordered pairs) on the graph. You can either use WINDOW to setup the window or press ZOOM 9:ZoomStat to adjust the window automatically. Press GRAPH to view the plot. Later you may also want to graph a regression equation with the plot. All you have to do is enter the equation in the Y= menu and press GRAPH. 4

5 Statistical Tests and Confidence Intervals STAT TESTS menu. Press STAT to highlight TESTS. 1: Z-Test... One sample z test. Performs a hypothesis test for a single unknown population mean µ, when σ is known. It tests H o : µ=µ o against one of the alternatives H a : µuµ o, H a : µ<µ o, H a : µ>µ o. 2: T-Test... One sample t test. Performs a hypothesis test for a single unknown population mean µ, when σ is unknown. It tests H o : µ=µ o against one of the alternatives H a : µuµ o, H a : µ<µ o, H a : µ>µ o. 3: 2-SampZTest... Two sample z test. Performs a hypothesis test for the equality of the two population means (µ 1 and µ 2 ) based on independent samples when both population standard deviations σ 1 and σ 2 are known. It tests H o : µ 1 =µ 2 against one of the alternatives H a : µ 1 Uµ 2, H a : µ 1 <µ 2, H a : µ 1 >µ 2. 4: 2-SampTTest... Two sample t test. Performs a hypothesis test for the equality of the two population means (µ 1 and µ 2 ) based on independent samples when neither population standard deviations σ 1 or σ 2 is known. It tests H o : µ 1 =µ 2 against one of the alternatives H a : µ 1 Uµ 2, H a : µ 1 <µ 2, H a : µ 1 >µ 2. 5: 1-PropZTest... One sample proportion z test. Performs a hypothesis test for an unknown proportion of successes (prop). X = Number of successes in the sample. N = Number of observations in the sample. It tests H o : prop=p o against one of the alternatives H a : propup o, H a : prop<p o, H a : prop>p o. 6: 2-PropZTest... Two sample proportion z test. Performs a hypothesis test to compare the proportion of successes (p 1 and p 2 ) from two populations. X1 = Number of successes in sample 1. X2 = Number of successes in sample 2. N1 = Number of observations in sample 1. N2= Number of observations in sample 2. It tests H o : p 1 =p 2 against one of the alternatives H a : p 1 Up 2, H a : p 1 <p 2, H a : p 1 >p 2. 5

6 7: Z-Interval... One sample z confidence interval. Computes a confidence interval for an unknown population mean µ when the population standard deviation σ is known. 8: T-Interval... One sample t confidence interval. Computes a confidence interval for an unknown population mean µ when the population standard deviation σ is unknown. 9: 2-SampZInt... Two sample z confidence interval. Computes a confidence interval for the difference between two population means (µ 1 - µ 2 ) when both population standard deviations (σ 1 and σ 2 ) are known. 0: 2-SampTInt... Two sample t confidence interval. Computes a confidence interval for the difference between two population means (µ 1 - µ 2 ) when both population standard deviations (σ 1 and σ 2 ) are unknown. A: 1-PropZInt... One sample proportion z confidence interval. Computes a confidence interval for an unknown proportion of successes. X = Number of successes in the sample. N = Number of observations in the sample. B: 2-PropZInt... Two sample proportion z confidence interval. Computes a confidence interval for the difference between two population proportions (p 1 - p 2 ). X1 = Number of successes in sample 1. X2 = Number of successes in sample 2. N1 = Number of observations in sample 1. N2= Number of observations in sample 2. C: χ 2 -Test... Test of Independence between two qualitative variables. It tests H o : two variables are independent against H a : the two variables are related. Before conducting the test, enter the observed counts in matrix [A]. The calculator will compute the expected counts and store them in matrix [B]. E: LinRegTTest... Linear regression t test. Computes a linear regression and a t test on the slope β and the correlation coefficient ρ for the equation y = α+βx. It tests H o : β=0 (ρ=0) against one of the alternatives H a : βu0 (ρu0), H a : β<0 (ρ<0), H a : β>0 (ρ>0). Here are some examples. Z-Test: Since the default 1:Z-Test is highlighted, just press ENTER. Use the arrows to choose either Data (you must enter the data in a list) or Stats (you will be asked for and n). See the two screens below. 6

7 Type in the requested information pressing to move to the next line. On the line with µ select the direction of the test you wish to perform. Use to highlight the appropriate choice and press ENTER to activate it. Press and choose either Calculate or Draw and press ENTER. If you choose the Draw option be sure you have turned all plots off. Calculate: Draw: T-Interval: Press STAT to highlight TESTS, then press 8 for T-Interval. Use the arrows to choose either Data (you must enter the data in a list) or Stats (you will be asked for, s x, and n). See the two screens below. Type in the requested information pressing to move to the next line. When you get to Calculate, press ENTER to compute the confidence interval. 7

8 Probability Combinations and Permutations are located in the MATH menu. To use these features you need to start from the home screen. Type in the value for n then press MATH to highlight PRB Press either 2 (for permutation) or 3 (for combination). The command is copied to the home screen. Now type in the value for r and press ENTER. DISTR menu DISTR 1: normalpdf( Computes the probability for the normal distribution at a specified x value. The defaults are mean µ = 0 and standard deviation σ = 1. This is mainly used to plot the normal distribution. In the Y= menu select normalpdf( Y 1 =normalpdf(x,µ,σ) [fill in the values for µ and σ] 2: normalcdf( Computes the normal distribution probability between lowerbound and upperbound for the specified mean µ and standard deviation σ. Use -1E99 to specify -" and 1E99 to specify ". normalcdf(lowerbound,upperbound,µ,σ) 8

9 0: binompdf( Computes a probability at x for the binomial distribution with n trials and probability of success p on each trial. If you do not specify x, a list of probabilities from 0 to n is returned. Binompdf(n,p,x) A: binomcdf( Computes a cumulative probability at x for the binomial distribution with n trials and probability of success p on each trial. If you do not specify x, a list of cumulative probabilities from 0 to n is returned. Binomcdf(n,p,x) DISTR DRAW menu 1: ShadeNorm( Draws the normal distribution with mean µ and standard deviation σ and shades the area between lowerbound and upperbound.. Use -1E99 to specify -" and 1E99 to specify ". Be sure to set your window before you execute the ShadeNorm command. ShadeNorm(lowerbound,upperbound,µ,σ). 9