MATH200B
Program OverviewMATH200B
Program Overview2nd
x,T,θ,n
makesLINK
][►
] [ENTER
]. Then on hers press[2nd
x,T,θ,n
makesLINK
] [3
], selectMATH200B (or M20083B; see above),and finally press [►
] [ENTER
].If you get a prompt about a duplicate program, choose Overwrite.PRGM
] key. If you can see MATH200B
in the menu, press its number; otherwise, scroll to it and press[ENTER
]. When the program name appears on your home screen,press [ENTER
] a second time to run it. Check the splash screen to make sure you have thelatest version (v4.4a), then press[ENTER
].Skew/kurtosis
:compute skewness and kurtosis, which arenumerical measures of the shape of a distributionTime series
:plot time-series dataCritical t
:find the t value that cuts thedistribution with a given probability in the right-hand tailCritical χ²
:find the χ² value that cuts thedistribution with a given probability in the right-hand tailInfer about σ
:hypothesis tests and confidence intervals forpopulation standard deviation and varianceCorrelatn inf
:hypothesis tests and confidence intervalsfor the linear correlation of a population; the hypothesis test forcorrelation doubles as a hypothesis test for slope of the regressionlineRegression inf
:confidence intervals for slope of theregression line, y intercept, and ŷ for a particular x, plusprediction intervals for ŷ for a particular xON
] [1
].1:Skew/kurtosis
part of the MATH200B
program computes these statisticsfor a list of numbers or a grouped or ungrouped frequencydistribution. This section of the document explains how to use theprogram and how to interpret the numbers.PRGM
], scroll if necessary and selectMATH200B
, and in the program menu select 1:Skew/kurtosis
. Specify yourdata arrangement, enter your data list, and if appropriate enter yourfrequency or probability list. The program will produce a great manystatistics.Class boundaries | 59.5–62.5 | 62.5–65.5 | 65.5–68.5 | 68.5–71.5 | 71.5–74.5 |
---|---|---|---|---|---|
Class midpoints, x | 61 | 64 | 67 | 70 | 73 |
Frequency, f | 5 | 18 | 42 | 27 | 8 |
Data are adapted fromSpiegel 1999 [full citation in “References”, below], page 68. |
MATH200B
program and select 1:Skew/kurtosis
.Your data arrangement is 3:Grouped dist
.When prompted, enter the list that contains thex’s and then the list that containsthe f’s. I’ve used L5 and L6, but you could use any lists.Probability Distribution for Throwing Two Dice | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Spots, x | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
Probability, P(x) | 1/36 | 2/36 | 3/36 | 4/36 | 5/36 | 6/36 | 5/36 | 4/36 | 3/36 | 2/36 | 1/36 |
MATH200B
program and select 1:Skew/kurtosis
. Your data arrangement is4:Discrete PD
,and you’ll see the following results:2:Time series
part ofthe MATH200B
program.Month | 3/03 | 4/03 | 5/03 | 6/03 | 7/03 | 8/03 | 9/03 | 10/03 |
---|---|---|---|---|---|---|---|---|
Closing | 12.98 | 15.00 | 16.41 | 16.79 | 19.49 | 19.14 | 19.59 | 20.93 |
Month | 11/03 | 12/03 | 1/04 | 2/04 | 3/04 | 4/04 | 5/04 | 6/04 |
Closing | 22.70 | 24.23 | 25.71 | 23.16 | 23.57 | 20.91 | 22.37 | 23.70 |
Month | 7/04 | 8/04 | 9/04 | 10/04 | 11/04 | 12/04 | 1/05 | 2/05 |
Closing | 20.92 | 18.76 | 18.10 | 19.21 | 18.75 | 19.32 | 18.04 | 17.42 |
MATH200B
program and select 2:Time series
. The program prompts youfor the data list. (Caution: The program assumes thetime intervals are all equal. If they aren’t, the horizontalscale will not be uniform and the graph will not be correct.)TRACE
] key and displaythe closing prices, scrolling back and forth with the[◄
] and [►
] keys. If you wantto jump to a particular month, say June 2004, the 16th month, type16
and then press [ENTER
].invT
function asthe TI-84 does, but if you need to find critical t or inverse t oneither calculator you can use this part of the MATH200B
program.MATH200B
program and select 3:Critical t
. Whenprompted, enter 27 for degrees of freedom and 0.025 for the area ofthe right-hand tail, as shown in the first screen. After a shortpause, the calculator gives you the answer: t(27,0.025) =2.05.MATH200B
program and select4:Critical χ²
. Enter the number of degrees offreedom and the area of the right-hand tail. Be patient: thecomputation is slow. But the program gives you the critical χ²value of 22.36, as shown in the second screen.MATH200B
program and select 5:Infer about σ
.When prompted, enter the standard deviation and size of the sample,pressing [ENTER
] after each one. If you know the variance ofthe sample rather than the standard deviation, use the square rootoperation since s is the square root of the variance s² (seeexample below).L
and H
incase you want to use them in further calculations. You can includethem in any formula by pressing [ALPHA
)
makesL
] and [ALPHA
^
makesH
].X
, D
, and P
in case you wish to usethem in further calculations. You can include them in any formula with[x,T,θ,n], [ALPHA
x-1
makesD
], and [ALPHA
8
makesP
].386 | 388 | 381 | 395 | 392 | 383 | 389 | 383 | 370 |
379 | 382 | 388 | 390 | 386 | 393 | 374 | 381 | 386 |
391 | 384 | 390 | 374 | 386 | 393 | 384 | 381 | 386 |
386 | 374 | 393 | 385 | 388 | 384 | 385 | 388 | 392 |
400 | 377 | 378 | 392 | 380 | 380 | 395 | 393 | 387 |
1-Var
Stats
to find the sample standard deviation,which is 6.42 g. Obviously this is greater than the targetstandard deviation of 5 g, but is it enough greater that you cansay the machine is not operating correctly, or could it have come froma population with standard deviation no more than 5 g?Your hypotheses areMATH200B
program and select5:Infer about σ
. Enter s:6.42 andn:45, and select 5:Test σ>const
. Enter 5for σ in H0.INFER ABOUT σ
menu you select4:Test σ≠const
.MATH200B
and select [2
] in the firstmenu. Enter s and n, and in the second menu select1:σ interval
with a C-level of 95 or .95.The results screen is shown at right.TInterval
. Just remember that for Sx
thecalculator wants the sample standard deviation, but you have thesample variance, which is s². Therefore you take the square rootof sample variance to get sample standard deviation, as shown in theinput screen at near right.MATH200B
program and select5:Infer about σ
. Enter s:√7.3 and n:100.Select 2:σ² interval
and enter C-Level:.95 (or95). The program computes the confidence interval for populationvariance as 5.6 ≤ σ² ≤ 9.9.Notice that the output screen shows the point estimate for variance, s²,and that as expected the confidence interval is not symmetric.MATH200B
program computes aconfidence interval about ρ or performs a hypothesis test totell whether there is correlation in the population.MATH200B
program and select 7:Regression inf
.Commuting Distances and Times | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Miles, x | 3 | 5 | 7 | 8 | 10 | 11 | 12 | 12 | 13 | 15 | 15 | 16 | 18 | 19 | 20 |
Minutes, y | 7 | 20 | 20 | 15 | 25 | 17 | 20 | 35 | 26 | 25 | 35 | 32 | 44 | 37 | 45 |
LinReg(ax+b)
command can tell youthat the correlation of the sample is 0.88. But what can you inferabout ρ, the correlation of the population? You can get a confidenceinterval estimate for ρ, or you can perform a hypothesis testfor ρ≠0.LinReg(ax_b) L1,L2
(or whichever lists containyour data). This computes the residuals automatically. You can thenplot them by following the procedure in Display the Residuals, part ofLinked Variables. As you see from the graph at right, theresiduals don’t show any problem features.2nd
STAT
makesLIST
][▲
], scroll to RESID
if necessary, andpress [ENTER
] [ENTER
]. The graph at right shows that theresiduals are approximately normally distributed.MATH200B
program and select 6:Correlatn inf
. Whenprompted, enter your x list and y list, select1:Conf interval
, and enter your desired confidencelevel, such as .95 or 95 for 95%.MATH200B
program and select 6:Correlatn inf
. Enter your x and ylists and select 2:Test ρ≠0
.MATH200B
program findsconfidence intervals for the slope β1 and intercept β0of the line that best fits the entire population of points, not just aparticular sample. It can also find aconfidence interval about the mean ŷ for a particular xand aprediction interval about all ŷ’s for a particular x.MATH200B
program performs as part ofthe 6:Correlatn inf
menu selection.LinReg(ax+b)
will show the bestfitting regression line for this particular sample, but what can you say aboutthe regression for all commuters at that company?MATH200B
program and select7:Regression inf
. Specify the two lists and your desired confdence level,such as .95 or 95 for 95%.