Answer with Two means hypothesis test 15. Are Quarters Now Lighter? Weights of quarters are carefully considered in the designof the vending machines that we have all come to know and love. Data Set 29 “Coin Weights"in Appendix B includes weights of a sample of pre-1964 quarters (n = 40, x = 6.19267 g,s = 0.08700 g) and weights of a sample of post-1964 quarters (n =W40, x = 5.63930 g,S = 0.06194 g).a. Use a 0.05 significance level to test the claim that pre-1964 quarters have a mean weight thatis greater than the mean weight of post-1964 quarters.b. Construct a confidence interval appropriate for the hypothesis test in part (a).c. Do post-1964 quarters appear to weigh less than before 1964? If so, why aren't vendingmachines affected very much by the difference?

Given n1=40, X1bar=6.19267, S1=0.087 n2=40, X2bar=5.6393, S2=0.06194 We want to test the hypothesis…

Answered: 15. Are Quarters Now Lighter? Weights…

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Answer with Two means hypothesis test

15. Are Quarters Now Lighter? Weights of quarters are carefully considered in the design
of the vending machines that we have all come to know and love. Data Set 29 “Coin Weights"
in Appendix B includes weights of a sample of pre-1964 quarters (n = 40, x = 6.19267 g,
s = 0.08700 g) and weights of a sample of post-1964 quarters (n =
W
40, x = 5.63930 g,
S = 0.06194 g).
a. Use a 0.05 significance level to test the claim that pre-1964 quarters have a mean weight that
is greater than the mean weight of post-1964 quarters.
b. Construct a confidence interval appropriate for the hypothesis test in part (a).
c. Do post-1964 quarters appear to weigh less than before 1964? If so, why aren't vending
machines affected very much by the difference?

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 + ...

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