A new material will replace the old material only if there is significant evidence that the mean strength of the new material is more than 2 units higher than the mean strength of the old material.        Sample from new material:     mean  is  98.064   ,     SD  is   5.6     and sample size is 13 Sample from old material:       mean  is  95.282   ,     SD  is   5.8      and sample size is 78 We do not know population standard deviations. Consider the test           ?0:????−????=2H0:μnew−μold=2   vs.  ?0:????−????>2H0:μnew−μold>2  What is the p-value?       (Hint:  best to use software, or else the Desmos Calculator for the 2 sample T and Z test)  Give as a decimal between 0 and 1 accurate to at least 4 decimal places.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...