User Manual
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Returns product of a list. Returns standard deviation of elements in list. For a complex list, the element with smallest or largest magnitude (modulus) is returned. Returns maximum element of elements in listA and ... of a list. Returns the variance of a list. If two lists are compared, it returns a list of the smaller or larger of each pair of listA. TI-83 Plus Lists 311 min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of elements in a list.
Returns product of a list. Returns standard deviation of elements in list. For a complex list, the element with smallest or largest magnitude (modulus) is returned. Returns maximum element of elements in listA and ... of a list. Returns the variance of a list. If two lists are compared, it returns a list of the smaller or larger of each pair of listA. TI-83 Plus Lists 311 min(, max( min( (minimum) and max( (maximum) return the smallest or largest element of elements in a list.
User Manual
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... 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 To evaluate G 2(N-1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. Complex lists are not valid. The default value for freqlist is 1. Complex lists are...
... 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 To evaluate G 2(N-1) from N=1 to 4: stdDev(, variance( stdDev( returns the standard deviation of the elements in list. Complex lists are not valid. The default value for freqlist is 1. Complex lists are...
User Manual
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... To access these variables for use in the column below . If you edit a list or change the type of x ... 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 ...standard deviation of y sum of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. y minimum 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...
... To access these variables for use in the column below . If you edit a list or change the type of x ... 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 ...standard deviation of y sum of analysis, all statistical variables are calculated and stored as indicated below under VARS menu. y minimum 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...
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 789). The 10 height values below . Height (in centimeters) of Each of a Population Getting Started is a fast-paced introduction. Because heights among a biological population ...: 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 789). The 10 height values below . Height (in centimeters) of Each of a Population Getting Started is a fast-paced introduction. Because heights among a biological population ...: 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
...), shows that you can enter summary statistics as input. The .99 confidence level indicates that in the calculated interval. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 The second line gives the mean height of the sample þ used to contain the population mean þ of...
...), shows that you can enter summary statistics as input. The .99 confidence level indicates that in the calculated interval. The third line gives the sample standard deviation Sx. TI-83 Plus Inferential Statistics and Distributions 384 The second line gives the mean height of the sample þ used to contain the population mean þ of...
User Manual
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... the DISTR (distributions) menu. 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. Press y = to clear... to move the cursor onto Calculate, and then press Í to n. 9. Press 7 Ë 1 Í to store 7.1 to ü. TI-83 Plus Inferential Statistics and Distributions 385 8. The results are displayed on the home screen. Press † 163 Ë 8 Í to store 163.8 to Sx.
... the DISTR (distributions) menu. 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. Press y = to clear... to move the cursor onto Calculate, and then press Í to n. 9. Press 7 Ë 1 Í to store 7.1 to ü. TI-83 Plus Inferential Statistics and Distributions 385 8. The results are displayed on the home screen. Press † 163 Ë 8 Í to store 163.8 to Sx.
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14. 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. TI-83 Plus Inferential Statistics and Distributions 387 Press Í to paste ShadeNorm( to plot and shade the normal curve. The normal curve is the upper bound. Area is the lower bound. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. low is the area above the 95th percentile. Press Í to the home screen. up is the upper bound.
14. 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. TI-83 Plus Inferential Statistics and Distributions 387 Press Í to paste ShadeNorm( to plot and shade the normal curve. The normal curve is the upper bound. Area is the lower bound. Press y Z ¢ 1 y D 99 ¢ 165 Ë 1 ¢ 6 Ë 35 ¤. low is the area above the 95th percentile. Press Í to the home screen. up is the upper bound.
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
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... alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) TI-83 Plus Inferential Statistics and Distributions 397 It tests the null hypothesis H0: m=m0 against one -sample t test; 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...
... alternatives below. • Ha: mƒm0 (m:ƒm0) • Ha: mm0) TI-83 Plus Inferential Statistics and Distributions 397 It tests the null hypothesis H0: m=m0 against one -sample t test; 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...
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; 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
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; The computed confidence interval depends on the user-specified confidence level.
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. 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; The computed confidence interval depends on the user-specified confidence level.
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 TInterval TInterval (one-sample t confidence interval; The computed confidence interval depends on the user-specified confidence level.
User Manual
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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 item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known. 2.SampZInt 2.SampZInt (two-sample z confidence interval;
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 item 9) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are known. 2.SampZInt 2.SampZInt (two-sample z confidence interval;
User Manual
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The computed confidence interval depends on the userspecified confidence level. item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. 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 Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval;
The computed confidence interval depends on the userspecified confidence level. item 0) computes a confidence interval for the difference between two population means (m1Nm2) when both population standard deviations (s1 and s2) are unknown. 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 Calculated results: 2.SampTInt 2.SampTInt (two-sample t confidence interval;
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
... data in the inferential stat editors. In tests, Draw draws a graph of the population mean , standard deviation, and sample size) for these inputs in List. TI-83 Plus Inferential Statistics and Distributions 419 You enter values for the one-sample tests and intervals. The known population... standard deviation; The name of output to generate for the two-sample tests and intervals. Determines the ...
... data in the inferential stat editors. In tests, Draw draws a graph of the population mean , standard deviation, and sample size) for these inputs in List. TI-83 Plus Inferential Statistics and Distributions 419 You enter values for the one-sample tests and intervals. The known population... standard deviation; The name of output to generate for the two-sample tests and intervals. Determines the ...
User Manual
Page 423
... n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the two-sample tests and intervals. No instructs the TI.83 not to pool the variances. x The count of...TI.83 to pool the variances. TI-83 Plus Inferential Statistics and Distributions 420 Must be an integer , 0. Pooled Specifies whether variances are L1 and L2, respectively. Defaults are to be pooled for the two-sample tests and intervals. All elements must be an integer > 0. Must be integers | 0. Input Description s2 The known population standard deviation...
... n1, v2, Sx2, Summary statistics (mean, standard deviation, and n2 sample size) for sample one for the two-sample tests and intervals. No instructs the TI.83 not to pool the variances. x The count of...TI.83 to pool the variances. TI-83 Plus Inferential Statistics and Distributions 420 Must be an integer , 0. Pooled Specifies whether variances are L1 and L2, respectively. Defaults are to be pooled for the two-sample tests and intervals. All elements must be an integer > 0. Must be integers | 0. Input Description s2 The known population standard deviation...
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
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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