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 = 40, = 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. 1. HYPOTHESES Ho : H1 : 2. SIGNIFICANCE LEVEL a = 0.05 3. CRITICAL VALUE(S) Indicate location of statistic and critical values on diagram! 4. TEST STATISTIC 5. DECISION 6. CONCLUSION There ( IS / IS NOT ) enough evidence to ( REJECT / SUPPORT ) the claim that 7. P-VALUE (from calculator)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 = 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
Ho: pre-1964 quarters have a mean weight that is greater than mean weight of post-1964 quarters. (mu1>mu2)
H1: pre-1964 quarters have a mean weight that is not greater than mean weight of post-1964 quarters. (mu<=mu2)
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