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In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a twO- sample t-interval. e COINS (2) MWX Two-Sample T-Test and CI: Coin1, Coin4 B COINS (2) MWX Two-Sample T-Test and Cl: Coin4, Coin Method Method mean of Coint Pz mean of Coind Difference u - Po L mean of Coin4 , mean of Coint Difference: u - Uz Equat vorionces ore ossumed for this anaiysis Equal voriances ore assumed for this analysis. Descriptive Statistics Descriptive Statistics Sample Coin1 Coind Mean StDev SE Mean 0.543 0.363 Sample Coin4 Coint 9 6.744 0.18 N Mean StDev SE Mean 5.614 0.14 0363 0543 5.614 0.14 6.744 0.18 Estimation for Difference Estimation for Difference Pooled 90% CI for StDev Difference 0474 (0.709, 1.551) Difference Pooled 90% Cl for Difference -1.130 1.130 StDev Difference 0.474 (-1.551. -0.709) Test Test Null hypothesis Alternative hypothesis H, ,- Hz # 0 He He - Hz = 0 Null hypothesis Alternative hypothesis T-Value DF P-Value Ho He - Hz = 0 T-Value DF P-Value 4,73 14 0.000 -4.73 14 0.000 (iv) What Would have been the outcome if you had obtained a 90% two-sample t-interval for E(X.) – E(X1) instead of for E(X1) – E((X.)? Justify your conclusion in terms of the derivative of the parameter transformation involved.

In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a twO- sample t-interval. e COINS (2) MWX Two-Sample T-Test and CI: Coin1, Coin4 B COINS (2) MWX Two-Sample T-Test and Cl: Coin4, Coin Method Method mean of Coint Pz mean of Coind Difference u - Po L mean of Coin4 , mean of Coint Difference: u - Uz Equat vorionces ore ossumed for this anaiysis Equal voriances ore assumed for this analysis. Descriptive Statistics Descriptive Statistics Sample Coin1 Coind Mean StDev SE Mean 0.543 0.363 Sample Coin4 Coint 9 6.744 0.18 N Mean StDev SE Mean 5.614 0.14 0363 0543 5.614 0.14 6.744 0.18 Estimation for Difference Estimation for Difference Pooled 90% CI for StDev Difference 0474 (0.709, 1.551) Difference Pooled 90% Cl for Difference -1.130 1.130 StDev Difference 0.474 (-1.551. -0.709) Test Test Null hypothesis Alternative hypothesis H, ,- Hz # 0 He He - Hz = 0 Null hypothesis Alternative hypothesis T-Value DF P-Value Ho He - Hz = 0 T-Value DF P-Value 4,73 14 0.000 -4.73 14 0.000 (iv) What Would have been the outcome if you had obtained a 90% two-sample t-interval for E(X.) – E(X1) instead of for E(X1) – E((X.)? Justify your conclusion in terms of the derivative of the parameter transformation involved.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a two- sample t-interval. COINS (21.MWX Two-Sample T-Test and CI: Coin1, Coin4 A COINS (2)MWX Two-Sample T-Test and Cl: Coin4, Coin1 Method Method mean of Coin1 Pa mean of Coind Difference u- 4 mean of Coin4 z mean of Coint Difference: - Vz Equal variances ore assumed for this analysis Equal variances ore assumed for this analysis Descriptive Statistics Descriptive Statistics Sample N Mean StDev SE Mean 0.543 0.363 Sample Coin4 Coint N Mean StDev SE Mean 5.614 0363 0.543 Coin1 Coin4 0 18 6.744 5.614 0.14 0.14 0 18 6.744 Estimation for Difference Estimation for Difference Pooled 90% Cl for StDev Difference 0474 (0709 1551) Pooled 90% Cl for Difference 1.130 Difference -1.130 StDev Difference 0.474 (-1.551. -0,709) Test Test Null hypothesis Alternative hypothesis H - Hz #0 T-Value DF P-Value He -z =0 Null hypothesis Ho - Uz =O Alternative hypothesis H h - Pa#0 DF P-Value 0.000 4.73 14 0.000 T-Value -4.73 14 (iv) What Would have been the outcome if you had obtained a 90% two-sample t-interval for E(X.) - E(X1) instead of for E(X,) - E(QX.)? Justify your conclusion in terms of the derivative of the parameter transformation involved.
Transcribed Image Text:In various places in this module, data on the silver content of coins minted in the reign of the twelfth-century Byzantine king Manuel I Comnenus have been considered. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and fourth coinage (variable Coin4) which was produced a number of years later. it was argued that the silver contents in both the first and the fourth coinages can be assumed to be normally distributed. The question of interest is whether there were differences in the silver content of coins minted early and late in Manuel's reign. You are about to investigate this question using a two- sample t-interval. COINS (21.MWX Two-Sample T-Test and CI: Coin1, Coin4 A COINS (2)MWX Two-Sample T-Test and Cl: Coin4, Coin1 Method Method mean of Coin1 Pa mean of Coind Difference u- 4 mean of Coin4 z mean of Coint Difference: - Vz Equal variances ore assumed for this analysis Equal variances ore assumed for this analysis Descriptive Statistics Descriptive Statistics Sample N Mean StDev SE Mean 0.543 0.363 Sample Coin4 Coint N Mean StDev SE Mean 5.614 0363 0.543 Coin1 Coin4 0 18 6.744 5.614 0.14 0.14 0 18 6.744 Estimation for Difference Estimation for Difference Pooled 90% Cl for StDev Difference 0474 (0709 1551) Pooled 90% Cl for Difference 1.130 Difference -1.130 StDev Difference 0.474 (-1.551. -0,709) Test Test Null hypothesis Alternative hypothesis H - Hz #0 T-Value DF P-Value He -z =0 Null hypothesis Ho - Uz =O Alternative hypothesis H h - Pa#0 DF P-Value 0.000 4.73 14 0.000 T-Value -4.73 14 (iv) What Would have been the outcome if you had obtained a 90% two-sample t-interval for E(X.) - E(X1) instead of for E(X,) - E(QX.)? Justify your conclusion in terms of the derivative of the parameter transformation involved.
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