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Using the TI 83/84

Using the TI 83/84. Summary Statistics. Press STAT, ENTER (for EDIT) If you do not see L1, scroll left. If you still don’t see it, press INSERT, 2 nd , L1 (this is the 1 key) If there are old data under L1: Press the up arrow, then CLEAR, ENTER

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Using the TI 83/84

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  1. Using the TI 83/84

  2. Summary Statistics • Press STAT, ENTER (for EDIT) • If you do not see L1, scroll left. If you still don’t see it, press INSERT, 2nd, L1 (this is the 1 key) • If there are old data under L1: • Press the up arrow, then CLEAR, ENTER • DON’T use DELETE, ENTER. This causes L1 to disappear instead. Use INSERT, 2nd, L1 to get it back. • Enter data values in L1 one at a time, pressing ENTER after each. • If you make an error, use the up or down arrows to highlight the error, then enter the correct value. Use the arrows to get to the bottom of the list for the next value, if necessary. • Be sure to press ENTER after the last data value.

  3. Summary Statistics, Continued • Press STAT, Right Arrow (for CALC), ENTER • Press ENTER (for 1-Var Stats) • Press ENTER again • Read results • The Standard Deviation is labeled Sx

  4. x1 x2 Normal Probablilities • Find P(90 < x < 105) if x follows the normal model with mean 100 and standard deviation 15: • P(90 < x < 105) = normalcdf( 90 , 105 , 100 , 15) = .378

  5. x Normal Quantiles • We must find a so that P(x < a) = 2% when x has a normal distribution with a mean of 100 and a standard deviation of 15. • With the TI 83/84: a = invNorm( .02, 100 , 15) = 69.2

  6. Calculating r and Regression Coefficients • The first time you do this: • Press 2nd, CATALOG (above 0) • Scroll down to DiagnosticOn • Press ENTER, ENTER • Read “Done” • Your calculator will remember this setting even when turned off

  7. Calculating r and Regression Coefficients Continued • Press STAT, ENTER • If there are old values in L1: • Highlight L1, press CLEAR, then ENTER • If there are old values in L2: • Highlight L2, press CLEAR, then ENTER • Enter predictor (x) values in L1 • Enter response (y) values in L2 • Pairs must line up • Press STAT, > (to CALC) • Scroll down to LinReg(ax+b), press ENTER, ENTER • Read a, b, r and r2

  8. Binomial Probabilities • To find binomial probability distribution values – probabilities for a particular number of successes, say 3 successes in 5 trials with the chance of success = .9: • Let n = 5, p = .9, and x = 3 (Note the order: n, p, x) • Press 2nd, DISTR [VARS] • Scroll down to 0 and press ENTER, or just press 0 • “binompdf(“ appears. Press 5, .9, 3 ) ENTER(Note that the commas are required, and note the order: n, p, x) • .0729 appears • If the values for x = 2, 3, and 4 are all needed • Press 2nd, DISTR [VARS] • Scroll down to 0 and press ENTER, or just press 0 • “binompdf(“ appears. Press 5, .9, {2, 3, 4} ) ENTER • All 3 values appear • In general, press 2nd, DISTR, 0, then enter n, p, x

  9. Binomial Probabilities Continued • To find the binomial probability for a range of successes, say 3 or fewer successes in 5 trials with the chance of success = .9 : • Let n = 5, p = .9, and x = 3 • Press 2nd, DISTR [VARS] • Scroll down to A and press ENTER • “binomcdf(“ appears. Press 5, .9, 3 ) ENTER(Note that the commas are required) • .0815 appears • If the probability for fewer than 3 successes is needed: • Enter binomcdf(5, .9, 2 ); read .00856 • If the probability for more than 3 successes is needed: • Enter 1 - binomcdf(5, .9, 3 ); read .919

  10. Confidence Intervals for Proportions • Press STAT and use the cursor to highlight TESTS. • Scroll down to A: 1-PropZInt… and press ENTER. • The TI remembers your previous problem and shows the entries for it. You will overwrite these with the new entries. After x: enter the number of successes in the sample. • After n: enter the sample size. • After C-Level: enter the confidence level as a decimal fraction. • When the cursor blinks on Calculate, press ENTER again.

  11. Hypothesis Test for Proportions .93 • Of 4276 households sampled, 4019 had telephones. Test, at the 1% level, the claim that the percentage of households with telephones is now greater than 93%.  = .01 Claim: p > .93 H0: p< .93 (or p = .93) HA: p > .93 Press STAT, TESTS, 1-PropZTest, Enter 11

  12. Hypothesis Test for Proportions, Continued Test Performed .93 HA 2.54 z-score .00560 p-Value Sample Estimate for p .940 Sample Size • Of 4276 households sampled, 4019 had telephones. Test the claim that the percentage of households with telephones is greater than the 93%. H0: p< .93 (or p = .93) HA: p > .93 12

  13. Example: For the racial profiling sample data, use a 0.05 significance level to test the claim that the proportion of black drivers stopped by the police is greater than the proportion of white drivers who are stopped. Hypothesis Test for Two Proportions x z We have that: nB= 200xB = 24 On the TI-83/84: Press STAT, arrow to TESTS and scroll down to 2-PropZTest. Press Enter. nW= 1400 xW= 147 Make these entries: And, H0: pB≤pWHA: pB > pW Highlight Calculate and press ENTER 13

  14. Hypothesis Test for Two Proportions, Continued Your TI screen should look like this: This is HA This is the p- value. This is p If you press the down arrow twice, the TI will tell you the sample sizes, as a check. 14

  15. n = 106 y = 98.20o s = 0.62o  = 0.05 Confidence Interval for a Mean 15

  16. Hypothesis Test for a Mean 16

  17. Hypothesis Test for Two Means Press STAT and arrow over to TESTS. Scroll down to 2-SampTTest and press ENTER. Highlight STATS and press ENTERSet μ0: 0 Enter McGwire’s stats for sample 1 Enter Bonds’s stats for sample 2 Highlight HA as μ1: ≠ μ2 Your screen should look like this: McGwire n1 70 x1 418.5 s1 45.5 Select Pooled: No Select Calculate Press ENTER Bonds n2 73 x2 403.7 s2 30.6

  18. Hypothesis Test for Two Means, Continued Your screen should look like this: HATest StatisticP-Value Scrolling down reveals some to the statistics you entered earlier. The sample data support the claim that there is a difference between the mean home run distances of Mark McGwire and Barry Bonds. Because the P-value is less than .05, we reject The Null Hypothesis

  19. (x1 –x2) – E < (µ1 – µ2) < (x1 –x2) + E Confidence Interval for Two Means Using the sample data given in the preceding example, construct a 95%confidence interval estimate of the difference between the mean home run distances of Mark McGwire and Barry Bonds. We need E so that As before, Press STAT, go to TESTS, and now scroll down to 2-SampTInt and press ENTER. The TI remembers the entries from the last time 2-SampTTest or 2-SampTInt was used. Since these are the same, we need only scroll down to C-Level to make sure it is set to .95 (NOT 95%!). Pooled is always No for our work. Highlight CALCULATE and press ENTER.

  20. Matched Pairs Test TI-83/84 users may test paired sample hypotheses from raw data as follows:STAT EDIT Highlight L1 CLEAR ENTER Enter first half of each pair in L2 Enter second half of each pair in L3 2nd QUIT 2nd L2 – 2nd L3 STO> 2nd L1 Highlight L2 CLEAR ENTER STATTESTS2: T-TestHighlight DataENTERProceed as for one-samplet - Test Highlight L3 CLEAR ENTER

  21. Matched Pairs Test, Continued Claim: there is a difference between the actual low temperatures and the low temperatures that were forecast five days earlier That is, μd ≠ 0 H0: d = 0 H1: d  0

  22. Matched Pairs Confidence Interval Follow the instructions given above for entering the 2 samples into L2 and L3, then storing the difference in L1. We now need only compute a one-sample confidence interval using STATTESTSTIntervalENTERDataList: L1Freq: 1C-Level: .95CalculateENTER

  23. Goodness-of-Fit Test 1. STAT, EDIT, CLEAR L1, L2 and L3 5. STAT, CALC, 1-Var Stats, ENTER.Write down value of Σx 2. Enter observed counts in L2. 3. Enter expected counts in L3. 6. 2nd, DISTR, 8:X2cdf, ENTER, Σx, 1000, k-1) Read P-Value

  24. Test for Homogeneity Claim: There is no difference in the distribution of the continent of origin for student and staff cars. H0: There is no difference in the distribution of the continent of origin for student and staff cars.HA: There is a difference in the distribution of the continent of origin for student and staff cars. Set α = .05

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