# Instructions for : TI83, 83-Plus, 84-Plus for STP classes, Ela Jackiewicz

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1 Computing areas under normal curves: option 2 normalcdf(lower limit, upper limit, mean, standard deviation) will give are between lower and upper limits (mean=0 and St.dev=1 are default values) Ex1 To find area between 1 and 1.7 onder N(0,1) use normalcdf(1,1.7,0,1)=.1141 Ex2 To find area onder N(0,1) left of 2.3 use normalcdf( , 2.3,0,1)=.9893 (use any large negative number as lower limit) Ex3 To find area right of 2.11 under N(0,1) use normalcdf(2.11, ,0,1)=.0174 (use any large positive number as upper limit) Ex4 To find area under curve N(12,3) between 10 and 16 use normalcdf(10, 16, 12,3)=.6563 Finding points from under the normal curves when area is given. option 3 invnorm(area to the left, mean, standard deviation) (mean=0 and St.dev=1 are default values) Ex5 To find third decile of N(0,1) use invnorm(.3,0,1)=-.52 Ex6 To find 95 th percentile of N(0,1) (or to find Z. 05 ) use invnorm(.95,0,1)=1.645 Ex7 To find third quartile on N(12,3) use invnorm(.75,12,3)=14.02 Computing areas under t and chi-square curves: tcdf (lower limit, upper limit, degrees of freedom) 2 cdf(lower limit, upper limit, degrees of freedom) Deal with infinity the same as with normalcdf

2 Finding points from under the t- curves when area is given. invt(area to the left, degrees of freedom) Some older calculators do not have that option. Computing Confidence Intervals for one population Mean: Z interval procedure: (σ is known, normal population or a large sample) option7 is Zinterval Ex8 To find 90% CI for µ if X =17 n=10 and σ =4 use ZInterval σ:4 hit Enter interval is:(14.919,19.081) T interval procedure: (σ is unknown, normal population or a large sample) option8 is TInterval Ex9 To find 90% CI for µ if TInterval S:3.7 X =17 n=10 S=3.7and use hit Enter interval is:(14.855,19.145) Ex10 To find 90% CI for µ when σ is unknown if you have data given: 45,34,71,39 Use STAT menu then EDIT then input your data on any list (for ex L1)

3 Then Option8 is Tinterval Inpt: Data List:L1 (use 2 nd 1 to input L1) Freq:1 hit Enter interval is:(27.882,66.618) Ex11 To find 90% CI for µ when σ is unknown if you have data given in a frequency table : x frequency Use STAT menu then EDIT then input your data on any two lists (for ex x on L1 and frequency on L2) Then Option8 is Tinterval Inpt: Data List:L1 (use 2 nd 1 to input L1) Freq:L2 (use 2 nd 2 to input L2) hit Enter interval is:(30.95,39.964) Data option will work in a similar way for Zinterval procedure. 2 Sample T interval option10 is 2-SampleTInterval Use Stats option then input sample means, st. deviations and sizes, If Pooled Yes is selected, pooled test is performed, otherwise non pooled test is done. 1 Proportion Z interval option A is 1-PropZInterval It will use p-hat =x/n as estimate of p, just input x and n

4 2 Proportions Z interval option B is 2-PropZInterval It will use p-hat method, just input x and n for each population Conducting hypothesis tests for one population Mean: Z test procedure: (σ is known, normal population or a large sample) option 1 is Z-test Ex12 Test H 0 µ=15 vs H a µ>15, use =.05, data gives X =17 n=10 and σ =4, use Z-test µ 0 = 15 σ:4 µ: >µ 0 hit Enter, you get z=1.58, p=.056 (p-value), do not reject H 0 since p>.05 T test procedure: (σ is unknown, normal population or a large sample) option 2 is T-test Ex13 Test H 0 µ=15 vs H a µ>15, use =.05, data gives X =17 n=10 and S=2.7, use T-test µ 0 = 15 S x : 2.7 µ: >µ 0 hit Enter, you get t=2.34, p=.022 (p-value), reject H 0 since p<.05

5 Data option for Z-Interval and T-interval will work similar to the same option in the CI procedures (Ex 10 and 11) Testing other Hypothesis All tests are available in STATS TESTS option: Tests for 2 populations means: 2-SampTTest (select POOLED YES or NO) Test for paired samples: T-test, use 0 =0 In each test procedure Data option can be used if sample statistics are not computed. It works the same as confidence intervals procedures. Test for 1 population proportion: 1-PropZTest Test for 2 populations proportions: 2-PropZTest Chi-square test of independence: 1. Use MATRIX menu to put observed frequencies in a matrix 2. Use 2 Test, it is a nondirectional test, divide p-value by 2 for appropriate directional one Chi-square GOF Test: only newer calculators; 1. Place observed and expected frequencies on 2 different lists, (STAT EDIT option) 2. Use 2 GOF Test Computing probabilities for a Binomial Random Variable. Let X be binomial random variable, p=.43, n=25 (X= number of successes in 25 Bernoulli trials with probability of success p=.43) option 10: binompdf(n, p,k) computes probability that X=k option A: binomcdf(n,p,k) computes probability of X k Ex 14 a) Compute P(X=5)= binompdf(25,.43, 5)= b) Compute P(X 5)= binomcdf(25,.43, 5)=.0144 c) Compute P(X>5)=1- P(X 5)= 1-binomcdf(25,.43, 5)=.9856

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