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A certain piece of machinery is known to fail according to a Poisson process.
a) In a series of tests, the piece was let operate till failure, repaired immediately, and let operate till next failure and so on for 3 months. The total number failures observed were 3. If the intent of the test was to determine , was the test run for too long, too short or just about the appropriate length of time ?
b) To minimize unscheduled shutdowns, the piece of machinery is to be inspected and maintained on a regular interval of X days. What X should you select to have 90% confidence that you will not see failures during operation?
c) Based on the results from (b), estimate the likelihood of finding no failure in 2 consecutive time periods.
d) Based on your results from (a) assign a probability distribution to  and update it by taking to account that you found no unscheduled shutdowns, under the maintenance schedule you found in (b) for 3 months.
A 95% confidence interval for the proportion of all adults who bought a lottery ticket in the past year is (assume Gallup used an SRS)
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For the sample of men, performance on the simulator task declined by an average of 2.9 points with s = 4.1. Is this a statistically significant change? Use a two-tailed test with = .05.
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The following data represent the number of weed-eaters sold per month at a local garden shop and their prices
a) Do a test to see if workers attitudes on this matter have changed using a 90% alpha. b) Explain to management what your findings are and what this suggests about future decisions vs work options.
a) What is the purpose of sampling? b) What are some concerns and dangers of sampling?
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