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Problem 3. Remember that cesium-134 atoms are radioactive, and the time until an atom decays has an exponential distribution with A = 0.33485yr_1 (corresponding to a half-life of 2.07 years). You have a collection of 100 radioactive atoms, but you don't know whether they are cesium134 or something else. So, you measure the decay times of 52 of the atoms, and compare their average decay time to that of cesium-134. You suspect that they are cesium-134, and will continue to believe this unless you have strong evidence to the contrary (you want to perform the test with a signicance level of 0.10). Here are the results from your test (decay times measured in years; yes, you are very patient.) 1.41 1.45 1.55 1.60 1.60 1.67 1.69 1.71 1.75 1.78 1.78 1.81 1.82 1.83 1.83 1.90 1.92 1.94 2.00 2.00 2.08 2.08 2.10 2.15 2.35 2.75 2.75 2.80 2.83 3.00 3.00 3.16 3.17 3.17 3.25 3.35 3.39 3.50 3.50 3.50 3.67 4.00 4.00 4.13 4.17 4.75 5.00 5.10 5.18 5.44 5.50 5.70 (a) What are your null and alternative hypotheses? (b) What do you conclude about these atoms? (You may want to use a spreadsheet to save a lot of calculator work.) (c) What is the P-value associated with your test statistic