1 Stats on the TI 83 and TI 84 Calculator Entering the sample values Example: Sample data are {5, 10, 15, 20} 1. Press “2ND” and Left bracket button. 2. Enter 5, press the comma button. 3. Enter 10, press the comma button. 4. Enter 15, press the comma button. 5. Enter 20, press “2ND” and Right bracket button. 6. Press the Store button. 7. Press “2ND” and the L1 button. 8. Press the ENTER button. The sample values are now stored in list L1. Left bracket {Right bracket } Store (STO)List L1 STAT buttonComma Enter2 Descriptive Statistics 1. Press the STAT button. 2. Press the right arrow to CALC. 3. Press the ENTER key to select 1-Var Stats (one-variable statistics). 4. Press “2ND” and the L1 key (to find the descriptive stats for the values in list L1). 5. Press the ENTER button. You will see: = 12.5 (this is the sample mean) Σx = 50 (this is the sum of the sample values) Σx2 = 750 (this is the sum of each sample value squared) Sx = 6.455 (this is the sample standard deviation, s) σx = 5.590 (this treats the four values you entered as a population. We will never use this value in DSCI 2710.) n = 4 (this is the sample size - - the number of values you entered in list L1) By repeatedly pressing the down arrow button, you will also see: MinX = 5 (this is the minimum sample value) Q1 = 7.5 (this is the first quartile) Med = 12.5 (this is the sample median and agrees with the textbook median definition) Q3 = 17.5 (this is the third quartile) MaxX = 20 (this is the maximum sample value) Right arrow Down arrow3 Finding combinations Example: How many ways can you get 4 heads (and 6 tails) in 10 flips of a coin? The answer is 10C4. How to find: 1. Enter 10. 2. Press the MATH button and the right arrow button three times to get to PRB (probability). 3. Press the down arrow two times to get to nCr. 4. Press the ENTER button and then enter 4. 5. Press the ENTER button again and you should see the answer (210). There are 210 ways of getting four heads and six tails in 10 flips of a coin. Finding binomial probabilities Example: What is the probability of getting 4 heads in 10 flips of a fair coin? 1. Press “2ND” and the DISTR key (DISTR is an abbreviation of the word “distribution”). 2. Press the down arrow until you get to the 10th one. It is called binompdf(. (“pdf” stands for probability density function. We call it the probability mass function, PMF.) 3. Press the ENTER key. 4. Enter 10 (this is n), press the comma button, enter .5 (this is p), press the comma button, enter 4, press the right parenthesis button. Then press the ENTER button. 5. You should see the answer: .205 There is a 20.5% chance of getting 4 heads and 6 tails in 10 flips. Comment: This is written: P(X = 4) is .205, where X = number of heads in the 10 flips. MATH buttonDISTR button Right parenthesis )4 Finding cumulative binomial probabilities The previous procedure was used to find “equal to” binomial probabilities, as in Table A.1 in the textbook. To find cumulative probabilities (as in Table A.2), use the following procedure: Example: What is the probability of getting less than or equal to 4 heads (no more than 4 heads) in 10 flips of a fair coin? 1. Press “2ND” and the DISTR key (DISTR is an abbreviation of the word “distribution”). 2. Press the down arrow until you get to the 11th one. It is called binomcdf(. (“cdf” stands for cumulative distribution function.) 3. Press the ENTER key. 4. Enter 10 (this is n), press the comma button, enter .5 (this is p), press the comma button, enter 4, press the right parenthesis button. Then press the ENTER button. 5. You should see the answer: .377 There is a 37.7% chance of getting no more than 4 heads in 10 flips of a fair coin. Comment: This is written: P(X ≤ 4) is .377, where X = number of heads in the 10 flips. This binomial discussion is especially useful for values of n and p that don’t fit the binomial tables.5 Finding Poisson probabilities Example: What is the probability of observing 6 arrivals over a one-minute interval, where the number of arrivals follows a Poisson distribution with a mean of 5 arrivals per minute? 1. Press “2ND” and the DISTR key (DISTR is an abbreviation of the word “distribution”). 2. Press the down arrow until you get to the 12th one. It is called poissonpdf(. (“pdf” stands for probability density function. We call it the probability mass function, PMF.) 3. Press the ENTER key. 4. Enter 5 (this is the mean, µ), press the comma button, enter 6, press the right parenthesis button. Then press the ENTER button. 5. You should see the answer: .146 There is a 14.6% chance of observing exactly 6 arrivals over a one-minute interval. Comment: This is written: P(X = 6) is .146, where X = number of arrivals over a one-minute interval. Finding cumulative Poisson probabilities Comment: Since we do not have a cumulative Poisson table, you might find this especially useful. Example: What is the probability of observing 6 arrivals or less (no more than 6 arrivals) over a one-minute interval, where the number of arrivals follows a Poisson distribution with a mean of 5 arrivals per minute? 1. Press “2ND” and the DISTR key (DISTR is an abbreviation of the word “distribution”). 2. Press the down arrow until you get to the 13th one. It is called poissoncdf(. (“cdf” stands for cumulative distribution function.) 3. Press the ENTER key. 4. Enter 5 (this is the mean, µ), press the comma button, enter 6, press the right parenthesis button. Then press the ENTER button. 5. You should see the answer: .762 There is a 76.2% chance of observing no more than 6 arrivals over a one-minute interval. Comment: This is written: P(X ≤ 6) is .762, where X = number of arrivals over a one-minute interval.6 Finding areas under the Z (standard normal) curve Comment: These calculators give you the area between two values of Z. Example: Find the area between zero and 1.52. 1. Press “2ND” and the DISTR key (DISTR is an abbreviation of the word “distribution”). 2. Press the down arrow until you get to the 2nd one. It is called normalcdf(.
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