User Manual
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.... If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. TI-83 Plus Lists 311 Returns median of a list. Returns standard deviation of elements in list. Returns product of a list. Returns the variance of listA. Returns mean ( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Returns...
.... If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. TI-83 Plus Lists 311 Returns median of a list. Returns standard deviation of elements in list. Returns product of a list. Returns the variance of listA. Returns mean ( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Returns...
User Manual
Page 317
.... Complex lists are not valid. Complex lists are not valid. To evaluate G 2(N-1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 variance( returns the variance of the corresponding element in list. Each freqlist element counts the number of consecutive...
.... Complex lists are not valid. Complex lists are not valid. To evaluate G 2(N-1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 variance( returns the variance of the corresponding element in list. Each freqlist element counts the number of consecutive...
User Manual
Page 368
... variables are cleared. If you edit a list or change the type of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. Variables mean of x values sum of x values sum of x2 values sample standard deviation of x population standard deviation of x number of data points...of y values sum of y2 values sample standard deviation of y population standard deviation of y sum of x values 1.Var Stats v Gx Gx2 Sx sx n minX 2.Var Stats v Gx Gx2 Sx sx n w Gy Gy2 Sy sy Gxy minX Other VARS menu XY G G XY XY XY XY G G XY XY G XY TI-83 Plus Statistics 365
... variables are cleared. If you edit a list or change the type of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. Variables mean of x values sum of x values sum of x2 values sample standard deviation of x population standard deviation of x number of data points...of y values sum of y2 values sample standard deviation of y population standard deviation of y sum of x values 1.Var Stats v Gx Gx2 Sx sx n minX 2.Var Stats v Gx Gx2 Sx sx n w Gy Gy2 Sy sy Gxy minX Other VARS menu XY G G XY XY XY XY G G XY XY G XY TI-83 Plus Statistics 365
User Manual
Page 384
Suppose you want to be normally distributed, a t distribution confidence interval can be used when estimating the mean of 165.1 centimeters and a standard deviation of 6.35 centimeters (randNorm(165.1,6.35,90) with a seed of women given the random sample below. The 10 height values below are the first 10 ...: Mean Height of 10 Women 169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53 TI-83 Plus Inferential Statistics and Distributions 381
Suppose you want to be normally distributed, a t distribution confidence interval can be used when estimating the mean of 165.1 centimeters and a standard deviation of 6.35 centimeters (randNorm(165.1,6.35,90) with a seed of women given the random sample below. The 10 height values below are the first 10 ...: Mean Height of 10 Women 169.43 168.33 159.55 169.97 159.79 181.42 171.17 162.04 167.15 159.53 TI-83 Plus Inferential Statistics and Distributions 381
User Manual
Page 387
...interval for TInterval. The actual mean þ of 163.8 and sample standard deviation Sx of women's heights, increase the sample size to compute this interval. The third line gives the sample standard deviation Sx. This time, use the Stats (summary statistics) input option. ...7. The bottom line gives the sample size n. The .99 confidence level indicates that in the calculated interval. To obtain a more precise bound on the population mean . TI-83 Plus Inferential Statistics and...
...interval for TInterval. The actual mean þ of 163.8 and sample standard deviation Sx of women's heights, increase the sample size to compute this interval. The third line gives the sample standard deviation Sx. This time, use the Stats (summary statistics) input option. ...7. The bottom line gives the sample size n. The .99 confidence level indicates that in the calculated interval. To obtain a more precise bound on the population mean . TI-83 Plus Inferential Statistics and...
User Manual
Page 388
... normally distributed with a mean m of 165.1 centimeters and a standard deviation σ of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)? 10. Press ' to n. 9. Press † to move the cursor onto Calculate, and then press Í to ü. TI-83 Plus Inferential Statistics and Distributions 385 Press † 163...
... normally distributed with a mean m of 165.1 centimeters and a standard deviation σ of 6.35 centimeters, what height is exceeded by only 5 percent of the women (the 95th percentile)? 10. Press ' to n. 9. Press † to move the cursor onto Calculate, and then press Í to ü. TI-83 Plus Inferential Statistics and Distributions 385 Press † 163...
User Manual
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Ans (175.5448205 from step 11) is the lower bound. 1å99 is defined by a mean µ of 165.1 and a standard deviation σ of 6.35. 15. The normal curve is the upper bound. 14. Press Í to paste ShadeNorm( to plot and shade the normal curve. low is the area above the 95th percentile. Area is the lower bound. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Press Í to the home screen. TI-83 Plus Inferential Statistics and Distributions 387 up is the upper bound.
Ans (175.5448205 from step 11) is the lower bound. 1å99 is defined by a mean µ of 165.1 and a standard deviation σ of 6.35. 15. The normal curve is the upper bound. 14. Press Í to paste ShadeNorm( to plot and shade the normal curve. low is the area above the 95th percentile. Area is the lower bound. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Press Í to the home screen. TI-83 Plus Inferential Statistics and Distributions 387 up is the upper bound.
User Manual
Page 399
Z.Test Z.Test (one of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 396 It tests the null hypothesis H0: m=m0 against one -sample z test; item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known.
Z.Test Z.Test (one of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 396 It tests the null hypothesis H0: m=m0 against one -sample z test; item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known.
User Manual
Page 400
... mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one -sample t test; Calculated results: Drawn results: Data , Stats , Note: All STAT TESTS examples assume a fixed-decimal mode setting of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) TI-83 Plus Inferential Statistics and Distributions...
... mean m when the population standard deviation s is unknown. It tests the null hypothesis H0: m=m0 against one -sample t test; Calculated results: Drawn results: Data , Stats , Note: All STAT TESTS examples assume a fixed-decimal mode setting of the alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) TI-83 Plus Inferential Statistics and Distributions...
User Manual
Page 402
item 3) tests the equality of the means of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) In the example: LISTA={154 109 137 115 140} LISTB={108 115 126 92 146} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 399 The null hypothesis H0: m1=m2 is tested against one of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. 2.SampZTest 2.SampZTest (two-sample z test;
item 3) tests the equality of the means of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) In the example: LISTA={154 109 137 115 140} LISTB={108 115 126 92 146} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 399 The null hypothesis H0: m1=m2 is tested against one of two populations (m1 and m2) based on independent samples when both population standard deviations (s1 and s2) are known. 2.SampZTest 2.SampZTest (two-sample z test;
User Manual
Page 403
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; The null hypothesis H0: m1=m2 is known. item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is tested against one of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) TI-83 Plus Inferential Statistics and Distributions 400
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; The null hypothesis H0: m1=m2 is known. item 4) tests the equality of the means of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is tested against one of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) TI-83 Plus Inferential Statistics and Distributions 400
User Manual
Page 408
In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , , Calculated results: TI-83 Plus Inferential Statistics and Distributions 405 The computed confidence interval depends on the user-specified confidence level. item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. ZInterval ZInterval (one-sample z confidence interval;
In the example: L1={299.4 297.7 301 298.9 300.2 297} Data Stats Input: , , Calculated results: TI-83 Plus Inferential Statistics and Distributions 405 The computed confidence interval depends on the user-specified confidence level. item 7) computes a confidence interval for an unknown population mean m when the population standard deviation s is known. ZInterval ZInterval (one-sample z confidence interval;
User Manual
Page 409
The computed confidence interval depends on the user-specified confidence level. TInterval TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. In the example: L6={1.6 1.7 1.8 1.9} Data Stats Input: , , Calculated results: TI-83 Plus Inferential Statistics and Distributions 406
The computed confidence interval depends on the user-specified confidence level. TInterval TInterval (one-sample t confidence interval; item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. In the example: L6={1.6 1.7 1.8 1.9} Data Stats Input: , , Calculated results: TI-83 Plus Inferential Statistics and Distributions 406
User Manual
Page 410
The computed confidence interval depends on the user-specified confidence level. 2.SampZInt 2.SampZInt (two-sample z confidence interval; In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 407 item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known.
The computed confidence interval depends on the user-specified confidence level. 2.SampZInt 2.SampZInt (two-sample z confidence interval; In the example: LISTC={154 109 137 115 140} LISTD={108 115 126 92 146} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 407 item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known.
User Manual
Page 411
item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval; The computed confidence interval depends on the userspecified confidence level. In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} TI-83 Plus Inferential Statistics and Distributions 408
item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval; The computed confidence interval depends on the userspecified confidence level. In the example: SAMP1={12.207 16.869 25.05 22.429 8.456 10.589} SAMP2={11.074 9.686 12.064 9.351 8.182 6.642} TI-83 Plus Inferential Statistics and Distributions 408
User Manual
Page 417
The population means and standard deviations are all unknown. 2.SampÜTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below. • Ha: s1ƒs2 (s1:ƒs2) • Ha: s1s2) In the example: SAMP4={ SAMP5={ 7 L4 18 17 L3 L5 1 10 11L2} L1 12 L1 L3 3 L5 5 2L11 L1L3} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 414 2.SampÜTest 2.SampÜTest (two-sample Û-test; item D) computes an Û-test to compare two normal population standard deviations (s1 and s2).
The population means and standard deviations are all unknown. 2.SampÜTest, which uses the ratio of sample variances Sx12/Sx22, tests the null hypothesis H0: s1=s2 against one of the alternatives below. • Ha: s1ƒs2 (s1:ƒs2) • Ha: s1s2) In the example: SAMP4={ SAMP5={ 7 L4 18 17 L3 L5 1 10 11L2} L1 12 L1 L3 3 L5 5 2L11 L1L3} Data Stats Input: , , TI-83 Plus Inferential Statistics and Distributions 414 2.SampÜTest 2.SampÜTest (two-sample Û-test; item D) computes an Û-test to compare two normal population standard deviations (s1 and s2).
User Manual
Page 422
... the list containing the frequency values for the two-sample tests and intervals. TI-83 Plus Inferential Statistics and Distributions 419 The name of the results. The known population standard deviation; Summary statistics (mean that they appear in this chapter. Calculate displays the ...in the same order that you are testing. All elements must be a real number > 0. Default=1. The known population standard deviation from the first population for the data in the inferential stat editors. Inferential Statistics Input Descriptions The tables in this section describe...
... the list containing the frequency values for the two-sample tests and intervals. TI-83 Plus Inferential Statistics and Distributions 419 The name of the results. The known population standard deviation; Summary statistics (mean that they appear in this chapter. Calculate displays the ...in the same order that you are testing. All elements must be a real number > 0. Default=1. The known population standard deviation from the first population for the data in the inferential stat editors. Inferential Statistics Input Descriptions The tables in this section describe...
User Manual
Page 423
... The expected sample proportion for the 2.PropZTest and 2.PropZInt. TI-83 Plus Inferential Statistics and Distributions 420 x1 The count of observations in the two- Defaults=1. Must be an integer , 0. Must be a real number, such that 0 < p0 < 1. Input Description s2 The known population standard deviation from sample one and sample two in the sample for...
... The expected sample proportion for the 2.PropZTest and 2.PropZInt. TI-83 Plus Inferential Statistics and Distributions 420 x1 The count of observations in the two- Defaults=1. Must be an integer , 0. Must be a real number, such that 0 < p0 < 1. Input Description s2 The known population standard deviation from sample one and sample two in the sample for...
User Manual
Page 425
Variables p-value test statistics degrees of freedom sample mean of x values for sample 1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for use in expressions, press , 5 (5:Statistics), and then... TEST Sx1, Sx2 n1, n2 Sx1, Sx2 n1, n2 TEST TEST SxP SxP SxP TEST Ç Ç TEST Ç1 Ç1 TEST Ç2 Ç2 TEST TI-83 Plus Inferential Statistics and Distributions 422
Variables p-value test statistics degrees of freedom sample mean of x values for sample 1 and sample 2 sample standard deviation of x for sample 1 and sample 2 number of data points for sample 1 and sample 2 pooled standard deviation estimated sample proportion estimated sample proportion for population 1 estimated sample proportion for use in expressions, press , 5 (5:Statistics), and then... TEST Sx1, Sx2 n1, n2 Sx1, Sx2 n1, n2 TEST TEST SxP SxP SxP TEST Ç Ç TEST Ç1 Ç1 TEST Ç2 Ç2 TEST TI-83 Plus Inferential Statistics and Distributions 422
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TI-83 Plus Inferential Statistics and Distributions 423 Variables confidence interval pair mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation Tests v Sx n LinRegTTest Intervals ANOVA lower, upper v Sx n s a, b r r2 RegEQ VARS Menu TEST XY XY XY TEST EQ EQ EQ EQ Note: The variables listed above cannot be archived.
TI-83 Plus Inferential Statistics and Distributions 423 Variables confidence interval pair mean of x values sample standard deviation of x number of data points standard error about the line regression/fit coefficients correlation coefficient coefficient of determination regression equation Tests v Sx n LinRegTTest Intervals ANOVA lower, upper v Sx n s a, b r r2 RegEQ VARS Menu TEST XY XY XY TEST EQ EQ EQ EQ Note: The variables listed above cannot be archived.