User Manual
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... a list. Returns product of a list. Returns standard deviation of a list. Returns the variance of a list. Returns maximum element of elements in listA and listB. If two lists are compared, it returns a list of the smaller or larger of each pair of a list. Returns median of listA. TI-83 Plus Lists 311 min(, max( min( (minimum...
... a list. Returns product of a list. Returns standard deviation of a list. Returns the variance of a list. Returns maximum element of elements in listA and listB. If two lists are compared, it returns a list of the smaller or larger of each pair of a list. Returns median of listA. TI-83 Plus Lists 311 min(, max( min( (minimum...
User Manual
Page 317
To evaluate G 2(N-1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. variance( returns the variance of the elements in list. Each freqlist element counts the number of consecutive occurrences of the ... value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 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. variance( returns the variance of the elements in list. Each freqlist element counts the number of consecutive occurrences of the ... value for freqlist is 1. Each freqlist element counts the number of consecutive occurrences of the corresponding element in list. stdDev(list[,freqlist]) variance(list[,freqlist]) TI-83 Plus Lists 314 Complex lists are not valid.
User Manual
Page 368
... under VARS menu. If you edit a list or change the type 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 To access these variables... for use in the column below . 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 mean of y values sum of y values sum...
... under VARS menu. If you edit a list or change the type 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 To access these variables... for use in the column below . 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 mean of y values sum of y values sum...
User Manual
Page 384
... height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed 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. Suppose you want to be normally distributed, 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 Read the chapter for details. Height (in centimeters) of Each of a Population Getting Started is a fast-paced ...
... height values below are the first 10 of 90 values, randomly generated from a normally distributed population with an assumed 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. Suppose you want to be normally distributed, 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 Read the chapter for details. Height (in centimeters) of Each of a Population Getting Started is a fast-paced ...
User Manual
Page 387
..., increase the sample size to contain the population mean height of the sample þ used to select Inpt:Stats. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 This is between about a 14.2 centimeters spread. Use a sample mean is about 159.74 centimeters and 173.94 centimeters...
..., increase the sample size to contain the population mean height of the sample þ used to select Inpt:Stats. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 This is between about a 14.2 centimeters spread. Use a sample mean is about 159.74 centimeters and 173.94 centimeters...
User Manual
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... 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. TI-83 Plus Inferential Statistics and Distributions 385 Press y = to Sx. Press † to move the cursor onto Calculate...
... 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. TI-83 Plus Inferential Statistics and Distributions 385 Press y = to Sx. Press † to move the cursor onto Calculate...
User Manual
Page 390
Ans (175.5448205 from step 11) is the lower bound. 1å99 is the lower bound. Press Í to the home screen. low is the upper bound. 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. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Area is the area above the 95th percentile. TI-83 Plus Inferential Statistics and Distributions 387 14. Press Í to paste ShadeNorm( to plot and shade the normal curve.
Ans (175.5448205 from step 11) is the lower bound. 1å99 is the lower bound. Press Í to the home screen. low is the upper bound. 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. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. Area is the area above the 95th percentile. TI-83 Plus Inferential Statistics and Distributions 387 14. Press Í to paste ShadeNorm( to plot and shade the normal curve.
User Manual
Page 399
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. 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
... test for a single unknown population mean m when the population standard deviation s is unknown. T.Test T.Test (one of 4 (Chapter 1). 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 397
... test for a single unknown population mean m when the population standard deviation s is unknown. T.Test T.Test (one of 4 (Chapter 1). 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 397
User Manual
Page 402
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; 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
User Manual
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Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; 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 The null hypothesis H0: m1=m2 is known.
Calculated results: , , Drawn results: 2.SampTTest 2.SampTTest (two-sample t test; 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 The null hypothesis H0: m1=m2 is known.
User Manual
Page 408
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. 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;
User Manual
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item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. TInterval TInterval (one-sample t confidence interval; 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
item 8) computes a confidence interval for an unknown population mean m when the population standard deviation s is unknown. TInterval TInterval (one-sample t confidence interval; 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
User Manual
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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; 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.
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. The computed confidence interval depends on the userspecified confidence level. Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval;
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. The computed confidence interval depends on the userspecified confidence level. Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval;
User Manual
Page 417
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). 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
User Manual
Page 422
...for these inputs in this chapter. In tests, Draw draws a graph of the population mean , standard deviation, and sample size) for tests and intervals. TI-83 Plus Inferential Statistics and Distributions 419 The name of the list containing the data you are testing. Determines the...in this section describe the inferential statistics inputs discussed in the inferential stat editors. Must be a real number > 0. The known population standard deviation from the first population for the data in this chapter. must be integers | 0. All elements must be a real number > 0....
...for these inputs in this chapter. In tests, Draw draws a graph of the population mean , standard deviation, and sample size) for tests and intervals. TI-83 Plus Inferential Statistics and Distributions 419 The name of the list containing the data you are testing. Determines the...in this section describe the inferential statistics inputs discussed in the inferential stat editors. Must be a real number > 0. The known population standard deviation from the first population for the data in this chapter. must be integers | 0. All elements must be a real number > 0....
User Manual
Page 423
... and 2.SampTInt. Must be an integer > 0. sample tests and intervals. Yes instructs the TI.83 to pool the variances. Must be a real number > 0. v1, Sx1, n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the 2.PropZTest and 2.PropZInt. Must be... of successes from the second population for the 1.PropZTest and 1.PropZInt. x1 The count of observations in the two- TI-83 Plus Inferential Statistics and Distributions 420 List1, List2 The names of the lists containing the data you are testing for 1.PropZTest.
... and 2.SampTInt. Must be an integer > 0. sample tests and intervals. Yes instructs the TI.83 to pool the variances. Must be a real number > 0. v1, Sx1, n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the 2.PropZTest and 2.PropZInt. Must be... of successes from the second population for the 1.PropZTest and 1.PropZInt. x1 The count of observations in the two- TI-83 Plus Inferential Statistics and Distributions 420 List1, List2 The names of the lists containing the data you are testing for 1.PropZTest.
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 ...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 ...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
User Manual
Page 426
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. TI-83 Plus Inferential Statistics and Distributions 423