at Ask Copilot ++ ponse-content-disposition=inline%3 Bfilename% of 5 (b) 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 full dataset is in the Minitab file coins.mwx. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and seven from the fourth coinage (variable Coin4) which was produced a number of years later. (For the purposes of this question, you can ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and Exercise 2 of Computer Book B, 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. (i) Using Minitab, find either the sample standard deviations of the two variables Coin1 and Coin4, or their sample variances. Hence check for equality of variances using the rule of thumb given in Subsection 4.4 of Unit 8. (ii) Whatever the outcome of part (c)(i), use Minitab to obtain a 90% two-sample t-interval for the difference E(X1) - E(X4), where X1 denotes the silver content in coins of the first coinage, and X4 denotes the silver content in coins of the fourth coinage. State that interval and comment briefly on what it tells us about the silver content of coins in the earlier and later coinages. [3] Q [3] (iii) Name the distribution used in constructing the confidence interval in part (c)(ii), state the value of its parameter, and show why the parameter takes the value that it does. [2] (iv) What would have been the outcome if you had obtained a 90% two-sample t-interval for E(X4) - E(X1) instead of for E(X1) E(X4)? Justify your conclusion in terms of the derivative of the parameter transformation involved. [3] F4 F5 $46 5 W ASUS F6 F7 & FO F10 F11 D F12 IA F8 7 Ca 8 a

at Ask Copilot ++ ponse-content-disposition=inline%3 Bfilename% of 5 (b) 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 full dataset is in the Minitab file coins.mwx. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and seven from the fourth coinage (variable Coin4) which was produced a number of years later. (For the purposes of this question, you can ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and Exercise 2 of Computer Book B, 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. (i) Using Minitab, find either the sample standard deviations of the two variables Coin1 and Coin4, or their sample variances. Hence check for equality of variances using the rule of thumb given in Subsection 4.4 of Unit 8. (ii) Whatever the outcome of part (c)(i), use Minitab to obtain a 90% two-sample t-interval for the difference E(X1) - E(X4), where X1 denotes the silver content in coins of the first coinage, and X4 denotes the silver content in coins of the fourth coinage. State that interval and comment briefly on what it tells us about the silver content of coins in the earlier and later coinages. [3] Q [3] (iii) Name the distribution used in constructing the confidence interval in part (c)(ii), state the value of its parameter, and show why the parameter takes the value that it does. [2] (iv) What would have been the outcome if you had obtained a 90% two-sample t-interval for E(X4) - E(X1) instead of for E(X1) E(X4)? Justify your conclusion in terms of the derivative of the parameter transformation involved. [3] F4 F5 $46 5 W ASUS F6 F7 & FO F10 F11 D F12 IA F8 7 Ca 8 a

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter7: Applying Fractions

Section7.6: Percents Problems

Problem 1WE

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(b) 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 full dataset is in the Minitab file coins.mwx. The dataset includes, among others, the values of the silver content of nine coins from the first coinage (variable Coin1) and seven from the fourth coinage (variable Coin4) which was produced a number of years later. (For the purposes of this question, you can ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and Exercise 2 of Computer Book B, 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. (i) Using Minitab, find either the sample standard deviations of the two variables Coin1 and Coin4, or their sample variances. Hence check for equality of variances using the rule of thumb given in Subsection 4.4 of Unit 8. [3] (ii) Whatever the outcome of part (c)(i), use Minitab to obtain a 90% two-sample t-interval for the difference E(X1) − E(X4), where X1 denotes the silver content in coins of the first coinage, and X4 denotes the silver content in coins of the fourth coinage. State that interval and comment briefly on what it tells us about the silver content of coins in the earlier and later coinages. [3] (iii) Name the distribution used in constructing the confidence interval in part (c)(ii), state the value of its parameter, and show why the parameter takes the value that it does. [2] (iv) What would have been the outcome if you had obtained a 90% two-sample t-interval for E(X4) − E(X1) instead of for E(X1) − E(X4)? Justify your conclusion in terms of the derivative of the parameter transformation involved. [3

at Ask Copilot
++
ponse-content-disposition=inline%3 Bfilename%
of 5
(b) 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 full dataset is in the Minitab file
coins.mwx. The dataset includes, among others, the values of the
silver content of nine coins from the first coinage (variable Coin1) and
seven from the fourth coinage (variable Coin4) which was produced a
number of years later. (For the purposes of this question, you can
ignore the variables Coin2 and Coin3.) In particular, in Activity 8 and
Exercise 2 of Computer Book B, 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.
(i) Using Minitab, find either the sample standard deviations of the
two variables Coin1 and Coin4, or their sample variances. Hence
check for equality of variances using the rule of thumb given in
Subsection 4.4 of Unit 8.
(ii) Whatever the outcome of part (c)(i), use Minitab to obtain a 90%
two-sample t-interval for the difference E(X1) - E(X4), where X1
denotes the silver content in coins of the first coinage, and X4
denotes the silver content in coins of the fourth coinage. State that
interval and comment briefly on what it tells us about the silver
content of coins in the earlier and later coinages.
[3]
Q
[3]
(iii) Name the distribution used in constructing the confidence interval
in part (c)(ii), state the value of its parameter, and show why the
parameter takes the value that it does.
[2]
(iv) What would have been the outcome if you had obtained a 90%
two-sample t-interval for E(X4) - E(X1) instead of
for E(X1) E(X4)? Justify your conclusion in terms of the
derivative of the parameter transformation involved.
[3]
F4
F5
$46
5
W
ASUS
F6
F7
&
FO
F10
F11
D
F12
IA
F8
7
Ca
8
a

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