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Examples Using the Stats/List Editor with the TI-89 PLUS Wm. J. Larson, [email protected], International School of Geneva upper value = 1 To enter Stats/List Editor key APPS Deg of Freedom = 6 ENTER. The Stats/List Editor screen has Auto-scale Yes four columns labeled list1 to list4. Mostly ENTER, ENTER however we will be using the F1 to F7 buttons at the top. The result is P(-1 t 1 and df = 6) = After leaving Stats/List Editor, for example .644, Which is 4% less than the normal after looking at the GRAPH screen or the Cdf above. HOME screen, you will need to key APPS ENTER again to reenter Stats/List ZInterval Editor. Example Calculate a confidence interval for using = 5, = 50, n = 25 and the desired Normal Cdf confidence level = 95%. Example For a normal distribution calculate Key F7 Ints [Notice that Stats/List editor can calculate P(x > 27| = 23, = 2). Key F5 Distr the confidence interval for seven [Notice that Statistics/List editor can different cases.] calculate the Pdf (probability distribution Key 1: ZInterval. function) & Cdf (cumulative probability Choose the Data Input Method = Stats, distribution function) for seven different since n, and are already known, distributions and can draw (Shade) and ENTER find the inverse for four of them.] Input Key 4: Normal Cdf =5 lower value = 27 = 50 upper value = n = 25 = 23 C Level = .95 =2 press ENTER Press ENTER, ENTER. The result is C Int {48.04, 51.96}, ME (the The result is P(x > 27| = 23, = 2) = Cdf margin of error = z*/n) = 1.96 = 0.0228 Example For a normal distribution calculate T-Test P(21 < x < 25| = 23, = 2). Example Test the hypothesis Ho: o = 10 Key F5 Distr, 4: Normal Cdf with Ha: o 10 using the data {8, 8, 9, 9, Enter 10, 11} using the t-distribution. lower value = 21 Key HOME upper value = 25 There are two ways to fill a list. We’ll use = 23 one method here & the other method =2 below. Press ENTER, ENTER In the HOME screen key {8, 8, 9, 9, 10, 11} The result is P(21 < x < 25| = 23, = 2) = STO VAR-LINK (2nd - ) List1 ENTER, Cdf = 0.683, which agrees with the 68ENTER 95-99.7 rule. Key APPS ENTER Notice that our data is now in list1. F6 Tests 2: T-Test Shade t Choose the Data Input Method. Since we Example Draw the Student t Distribution want to use the data we just entered, function and calculate the probability of choose Data. -1 t 1 with df (degrees of freedom) = 6. Input o = 10 Key F5 Distr 1: Shade 2: Shade t. List = VAR-LINK list1 lower value = -1 Freq = 1 (since each data point occurs once) Choose the alternative hypothesis o Results: choose Draw, ENTER The result is the t distribution with the tails shaded, t = -1.746 and the P-value = .141. So at the 10% level Ho cannot be rejected. [Calculate would have displayed the input values plus t, the P-value, df, , Sx and n.] Linear Regression & a Scatterplot Example Fit the following data to a straight line. Report the equation of the line, r² and r. Plot the equation on top of the data. Make a list of residuals. 1 2 3 4 5 x 23 24 25 24 27 y Key APPS ENTER In the list screen scroll up and right to an unnamed list. Key enter, type xlist and enter 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Scroll right to the next unnamed list. Key ENTER, type ylist (to name the list) and enter 23, 24, 25, 24, 27, 28, 30, 29, 35, 33. To get the list of residuals set F1 Tools 9: Format ResultsEditor to Yes. Key F4 Calc 3: Regressions. [Note that 11 Stats/List editor does 11 different kinds of regression.] Choose 1: LinReg(a+bx) Key X list = xlist, Y list = ylist Store RegEQ to y1(x) (So that you can plot the fitted line on top of your scatterplot.) Freq =1 (Since each data point occurs once.) Key ENTER The result is a = 20.9333, b = 1.24848, r² = .8832, r = .9398, so the line is a fairly good fit to the data. Note that the residuals are in a list called resid to the right of ylist, ready to be displayed as a scatterplot. Key F2 Plots 1: Plot Setup Highlight Plot 1 Key F1 Define Choose Plot Scatter Note that there are 4 other kinds of plots. 6 Select Mark 7 8 (or whatever 9 10 like) cross you 28Key x = 30xlist, y 29 35 33 = ylist Freq and Categories = No. ENTER Go to the Y = screen by keying Y = ( F1). As we expected, the regression equation is stored as y1 = 20.933 +1.248. Go to the GRAPH screen by keying GRAPH ( F3). Key F2 Zoom 9:ZoomData. There’s the data and the line. (F3 Trace ► or ◄ will read out each data point. ▲ or ▼ will take you back and forth between the scatterplot and the regression line.)