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# q4solutions - Statistics 20 Quiz 4 Solutions 1 A team of...

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Statistics 20: Quiz 4 Solutions 1. A team of doctors want to estimate the life expectancy of students afflicted with the rare genetic disease statinotisticitis ; however, only 15 known cases have ever been diagnosed. The sample reported a mean lifespan of 95 years with a standard deviation of 10. The doctors believe it’s reasonable to assume a Normal distribution for each data point. Construct a 95% confidence interval for life expectancy of patients with this disease. We may consider the life spans reported in the n = 15 known cases of the disease to be ran- dom variables X 1 , . . . , X 15 that are independent copies of X N ( μ, σ 2 ). We are interested in learning the life expectancy (or mean lifespan) μ . However, in this case the data’s standard deviation σ is unknown; the reported numbers for the mean and standard deviation are the estimates ¯ X and S . (It would indeed be difficult to know anything beyond these estimates when only 15 cases have ever been reported.) Because n is small, σ is unknown, and each data point follows a Normal distribution, we must use the t distribution with n - 1 = 15 - 1 = 14 degrees of freedom to construct a 95% confidence interval: 95% CI for μ = ¯ X ± t 14 df 0 . 95 S n - 1 = 95 ± 2 . 14 10 15 - 1 = (89 . 281 , 100 . 719). 2. A veterinarian wants to estimate the mean weight of full-grown calico cats. A previous study suggests assuming an SD of 3 pounds is reasonable. How many calicos should be surveyed to ensure with probability 0 . 95 that the maximum error is less than 0.1 pounds? (Round a decimal result up.)

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q4solutions - Statistics 20 Quiz 4 Solutions 1 A team of...

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