statistics Project

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REVIEW Statistics I on the TI83/84 (or Plus) for MTH 112 by Carla A. Monticelli

DISPLAY CONTRAST To increase the contrast, press and release [2nd], press and hold .

To decrease the contrast, press and release [2nd], press and hold . SETTINGS To change the mode settings: press [MODE] and use the arrow keys to highlight your selection. Press [ENTER] to select what you have highlighted. Press [2ND] [QUIT] to return to the home screen. OPERATIONS Many keys on the calculator have three functions: 1. What is written on the key in white lettering (just press the key). 2. What is written above left of the key in yellow or blue lettering (press [2nd ]and the

desired yellow function) 3. What is written above and to the right of the key in green lettering (press [alpha]

and the desired green symbol) EDITING

[ENTER] 23 To recall the last expression, press [2ND] [ENTRY]. To edit the expression, place the cursor over 4 and replace it with 7. [ENTER] 38 Recall the expresion again [2ND] [ENTRY] Press [del ] to delete 3 + Now use [2ND] [INS] to insert decimals: 7.1 * 5.2 [ENTER] 36.92 SUBTRACTION VS. OPPOSITE OF 5 [-]7 [ENTER] -2 [ (-)] 4 [ ] [ENTER] -16 TO ENTER DATA IN LISTS [STAT] [1:EDIT] Use arrows to move cursor to the desired list. Simply type a number and press enter. TO CLEAR LISTS On the home screen: [STAT] [4:CLRLIST] [2ND] [ ] [,] [2ND] [ ] [ENTER] Clears list 1 and 2. Note: Use commas to separate the lists. Clears all lists from the home screen: [2ND] [MEM] [4:ClrAllLists] [ENTER] When in the list mode: [STAT] [1:EDIT] highlight a list, press [CLEAR][ENTER] Clears one list at a time. Do not hit [DEL] If delete is pressed, the list itself is deleted. To get all the lists back: [STAT][5:SETUP EDITOR] [ENTER] ONE VARIABLE STATISTIC (raw data) Ex) enter 21 33 39 67 64 53 77 89 89 89 Data in list 1: [STAT][1:EDIT] Type each number then hit enter

[ ]D [ ]Ñ

3 4*5+

2x

1L 2L

2

To calculate statistics: To find the mean, median, quartiles, standard deviation for a single list:

TI 83 TI84 STAT STAT CALC CALC 1-Var Stats 1-Var Stats L1 List: L1 FreqList: leave blank

Calculate (enter) (See Mean = and standard deviation= ) ------------------------------------------------------------------------- To do a spreadsheet for standard deviation: Enter data in L1 Using the arrow keys, highlight L2 press [ENTER] Let L2 = L1 – 62.1 [ENTER] Using the arrow keys highlight L3 press [ENTER] Let L3 = [ENTER] To sum list three: [2ND] [QUIT] [2ND] [LIST] [>] [MATH] [5: SUM] [2ND] [ENTER]

To get variance: (KEEPING 24.88395288 on the screen), [ENTER] Variance = 619.21

62.1X = 24.88xS =

2 2L

[ ]3L

S = sum(x− x)2

n−1 = sum(L3) 10−1

= 5572.9 9

= 24.88

2Xé ùë û

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CONFIDENCE INTERVALS AND HYPOTHESIS TESTING The zinterval command computes a confidence interval for an unknown population mean when is known and either the population is normally distributed or n is at least 30. Press [STAT] [>] [TESTS] [7: zinterval Highlight STATS and press [ENTER] For test score data n=62 the sample mean is 60 and the population standard deviation is 10. For .95 degree of confidence, use these statistics to find the confidence interval for

the mean of the population.

EX) Test the claim that the mean test score is not 70. =.05 The ztest command performs a hypotheses test for a single unknown population mean when is known and either the population is normally distributed or n is at least 30. Press [STAT] [>] [TESTS] [1:Z-Test] Highlight STATS and hit [ENTER]

Z = -7.87 P= 3.5E -15 We reject H0 since p< .05. T-Test Command performs a hypotheses test for a single unknown population mean when is unknown and either the population is normally distributed or n is at least 30. Ex) In one part of a test developed by a psychiatrist, the test subject is asked to form a

word by unscrambling letters. Given are the times (in seconds) required by 15 randomly selected persons to unscramble letters (50, 16, 17, 50, 25, 52, 60, 40, 33, 30, 76, 16, 30, 74, 59) At the = .05 level of significance, test the claim that the mean time is equal to 50 seconds. Assume the population is normal.

Input the times into a list, say L1. Press [STAT] [>] [TESTS] [T-Test]

s

X s

a

s

s

a

4

Highlight DATA and press [ENTER] Input the following:

Highlight “calculate” and press enter. t= -1.57 p=.140 > do not reject Ho T-Interval Command calculates a confidence interval for a single unknown population mean when is unknown and either the population is normally distributed or n is at least 30. Let’s look at the confidence interval, since = .05 the c level is .95 [STAT] [>] [TESTS] [8:T-interval] highlight data and press [ENTER] highlight calculate and press [ENTER] Input the following:

Linear Correlation and Regression ONE TIME SET UP To turn “diagnostics” on and be able to see r and r2 [2nd] [Catalog] Diagnostics on Enter Enter To calculate r, r2:

TI 83 TI84 Stat Stat Edit Edit Enter x’s in L1 and y’s in L2 Enter x’s in L1 and y’s in L2 2nd Quit 2nd Quit Stat Stat >Calc >Calc 4:linreg 4:linreg L1, L2, Xlist: L1 Ylist: L2 FreqList: leave blank Store RegEQ: Calculate Note: To get above,

[VARS] [>] [YVARS] [1] for 1:Function] [1] for 1:

a

s

a

1Y

1Y

1Y

1Y

5

To generate a scatter plot for paired data: [2nd ][STAT PLOT] Choose 1: Plot1 (be sure STAT PLOT 2 & 3 are off) ON

Once the STAT PLOT is set up once you do not need to repeat. With data already entered in L1 and L2 Zoom 9:zoomstat