User Manual
Page 314
...Returns mean ( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Returns minimum element of a list. Returns sum of elements in a list. Returns standard deviation of a list. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. ...complex list, the element with smallest or largest magnitude (modulus) is returned. Returns median of elements in list. Returns product of a list. TI-83 Plus Lists 311 min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of a list. LIST MATH Menu ...
...Returns mean ( 4:median( 5:sum( 6:prod( 7:stdDev( 8:variance( Returns minimum element of a list. Returns sum of elements in a list. Returns standard deviation of a list. If two lists are compared, it returns a list of the smaller or larger of each pair of elements in listA and listB. ...complex list, the element with smallest or largest magnitude (modulus) is returned. Returns median of elements in list. Returns product of a list. TI-83 Plus Lists 311 min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of a list. LIST MATH Menu ...
User Manual
Page 317
... 4: stdDev(, variance( stdDev( returns the standard deviation of the corresponding element in list. Each freqlist element counts the number of consecutive occurrences of the elements in list. Each freqlist element counts the number of consecutive occurrences of the elements in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 variance( returns the...
... 4: stdDev(, variance( stdDev( returns the standard deviation of the corresponding element in list. Each freqlist element counts the number of consecutive occurrences of the elements in list. Each freqlist element counts the number of consecutive occurrences of the elements in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 variance( returns the...
User Manual
Page 368
To access these variables for use in the column below . If you edit a list or change the type of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. Statistical Variables The statistical variables ... of y values sum 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 y minimum of x ...
To access these variables for use in the column below . If you edit a list or change the type of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. Statistical Variables The statistical variables ... of y values sum 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 y minimum of x ...
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 90 values, randomly generated from a normally distributed population with an assumed mean . Because heights among a ...: 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 The 10 height values below .
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 90 values, randomly generated from a normally distributed population with an assumed mean . Because heights among a ...: 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 The 10 height values below .
User Manual
Page 387
... interval for TInterval. This is about 159.74 centimeters and 173.94 centimeters. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 Press ~ Í to display the inferential stat editor for the population mean þ of ...163.8 and sample standard deviation Sx of the sample þ used to 90. Use a sample mean is in a very large number ...
... interval for TInterval. This is about 159.74 centimeters and 173.94 centimeters. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 Press ~ Í to display the inferential stat editor for the population mean þ of ...163.8 and sample standard deviation Sx of the sample þ used to 90. Use a sample mean is in a very large number ...
User Manual
Page 388
TI-83 Plus Inferential Statistics and Distributions 385 Press † 163 Ë 8 Í to store 163.8 to Sx. If the height distribution among a population of women is 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. The...
TI-83 Plus Inferential Statistics and Distributions 385 Press † 163 Ë 8 Í to store 163.8 to Sx. If the height distribution among a population of women is 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. The...
User Manual
Page 390
Area is the lower bound. Press Í to the home screen. low is the area above the 95th percentile. 14. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. The normal curve is the upper bound. up is defined by a mean µ of 165.1 and a standard deviation σ of 6.35. 15. Ans (175.5448205 from step 11) is the lower bound. 1å99 is the upper bound. TI-83 Plus Inferential Statistics and Distributions 387 Press Í to paste ShadeNorm( to plot and shade the normal curve.
Area is the lower bound. Press Í to the home screen. low is the area above the 95th percentile. 14. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. The normal curve is the upper bound. up is defined by a mean µ of 165.1 and a standard deviation σ of 6.35. 15. Ans (175.5448205 from step 11) is the lower bound. 1å99 is the upper bound. TI-83 Plus Inferential Statistics and Distributions 387 Press Í to paste ShadeNorm( to plot and shade the normal curve.
User Manual
Page 399
item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one -sample z test; 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
item 1) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is known. It tests the null hypothesis H0: m=m0 against one -sample z test; 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
User Manual
Page 400
item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T....: 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 397
item 2) performs a hypothesis test for a single unknown population mean m when the population standard deviation s is unknown. If you set the decimal mode to Float or a different fixed-decimal setting, your output may differ from the output in the examples. T....: 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 397
User Manual
Page 402
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; 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.
User Manual
Page 403
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; item 4) tests the equality of the means of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) TI-83 Plus Inferential Statistics and Distributions 400 The null hypothesis H0: m1=m2 is tested against one of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known.
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; item 4) tests the equality of the means of the alternatives below. • Ha: m1ƒm2 (m1:ƒm2) • Ha: m1m2) TI-83 Plus Inferential Statistics and Distributions 400 The null hypothesis H0: m1=m2 is tested against one of two populations (m1 and m2) based on independent samples when neither population standard deviation (s1 or s2) is known.
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 ZInterval ZInterval (one-sample z confidence interval; 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.
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 ZInterval ZInterval (one-sample z confidence interval; 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.
User Manual
Page 409
item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. The computed confidence interval depends on the user-specified confidence level. 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 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. The computed confidence interval depends on the user-specified confidence level. 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 TInterval TInterval (one-sample t confidence interval;
User Manual
Page 410
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. 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 2.SampZInt 2.SampZInt (two-sample z confidence interval;
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. 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 2.SampZInt 2.SampZInt (two-sample z confidence interval;
User Manual
Page 411
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 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.
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
... name of the population mean , standard deviation, and sample size) for the data in this chapter. All elements must be a real number > 0. In tests, Draw draws a graph of the list containing the data you are testing. TI-83 Plus Inferential Statistics and Distributions 419 The... name of the results. Determines the type of output to generate for the two-sample tests and intervals. The known population standard deviation from the first population for tests and ...
... name of the population mean , standard deviation, and sample size) for the data in this chapter. All elements must be a real number > 0. In tests, Draw draws a graph of the list containing the data you are testing. TI-83 Plus Inferential Statistics and Distributions 419 The... name of the results. Determines the type of output to generate for the two-sample tests and intervals. The known population standard deviation from the first population for tests and ...
User Manual
Page 423
...number, such that 0 < p0 < 1. x1 The count of the lists containing the data you are L1 and L2, respectively. TI-83 Plus Inferential Statistics and Distributions 420 List1, List2 The names of successes from the second population for the two-sample tests and intervals. All elements..., Sx1, n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the 2.PropZTest and 2.PropZInt. No instructs the TI.83 not to be pooled for 2.SampTTest and 2.SampTInt. Yes instructs the TI.83 to pool the variances. Freq1, Freq2 The names of successes...
...number, such that 0 < p0 < 1. x1 The count of the lists containing the data you are L1 and L2, respectively. TI-83 Plus Inferential Statistics and Distributions 420 List1, List2 The names of successes from the second population for the two-sample tests and intervals. All elements..., Sx1, n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the 2.PropZTest and 2.PropZInt. No instructs the TI.83 not to be pooled for 2.SampTTest and 2.SampTInt. Yes instructs the TI.83 to pool the variances. Freq1, Freq2 The names of successes...
User Manual
Page 425
...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 ...TEST SxP SxP SxP TEST Ç Ç TEST Ç1 Ç1 TEST Ç2 Ç2 TEST TI-83 Plus Inferential Statistics and Distributions 422 Test and Interval Output Variables The inferential statistics variables are calculated as indicated below .
...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 ...TEST SxP SxP SxP TEST Ç Ç TEST Ç1 Ç1 TEST Ç2 Ç2 TEST TI-83 Plus Inferential Statistics and Distributions 422 Test and Interval Output Variables The inferential statistics variables are calculated as indicated below .
User Manual
Page 426
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.