Suppose the value of Young\'s modulus (GPa) was determined for cast plates consi

Question

Suppose the value of Young's modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations: 116.7 115.7 114.9 115.4 115.5 (a) Calculate x. GPa Calculate the deviations from the mean. (Enter your answers to two decimal places.) X 116.7 115.7 114.9 115.4 115.5 deviation (b) Use the deviations calculated in part (a) to obtain the sample variance and the sample standard deviation. (Round your answers to three decimal places.) s^2 = GPa^2 s = GPa (c) Subtract 50 from each observation to obtain a sample of transformed values. Now calculate the sample mean and sample variance of these transformed values. X_t = GPa s_t^2 = GPa^2 Compare the transformed x and s^2 to the original data. The transformed mean and variance are both the same as the original. The transformed mean is less than the original and the transformed variance is less than original variance. The transformed mean is less than the original but the transformed variance is the same original variance. The transformed mean is the same as the original but the transformed variance is less than the original variance. The transformed mean is less than the original and the transformed variance is greater than original variance.

Explanation / Answer

a)

mean = 116.7 + 115.7 + 114.9 + 115.4 + 115.5 / 5
= 115.64

deviation = (116.7 - 115.64)^2
= 1.1236
  
= (115.7 - 115.64)^2
= 0.0036

= (114.9 - 115.64)^2
= 0.5476

= (115.4 - 115.64)^2
= 0.0576

= (115.5 - 115.64)^2
= 0.0196

b) sample variance = 1.1236 + 0.0036 + 0.5476 + 0.0576+ 0.0196 / 4 = 0.438
  
sample std. devaition = sqrt(variance)
= sqrt(0.438) = 0.6618

c) Sample mean = 66.7 + 65.7 + 64.9 + 65.4+ 65.5 / 5
= 65.64
Sample variance = (66.7 - 65.54)^2 + (65.7 - 65.54)^2 + (64.9 - 65.54)^2 + (65.4 - 65.54)^2 + (65.5 - 65.54)^2
= 0.438

Answer is Option c )

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