.. ..Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of AdvancedManuf. Tech., 2010: 117-134)).(a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?E(X)GPa%3DGPa(b) Answer the questions posed in part (a) for a sample size of n = 64 sheets.E(X) =GPaGPa(c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning.X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of X that comes with a larger sample size.O x is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of X that comes with a smaller sample size.O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger sample size.O x is more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of X that comes with a smaller sample size.Need Help?Read ItMacBook Pro"0.3"&!@#$12478}PQWERTYU%3D

(a) The sampling distribution of X¯ centered is, EX¯=μ=70 Thus, the sampling distribution of X¯…

(a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) = GPa GPa

(a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) = GPa GPa

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

.. ..
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and
1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced
Manuf. Tech., 2010: 117-134)).
(a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?
E(X)
GPa
%3D
GPa
(b) Answer the questions posed in part (a) for a sample size of n = 64 sheets.
E(X) =
GPa
GPa
(c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning.
X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of X that comes with a larger sample size.
O x is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of X that comes with a smaller sample size.
O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger sample size.
O x is more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of X that comes with a smaller sample size.
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