Ghost of Speciation Past. In the article, “Ghost of Speciation Past” (Nature, Vol. 435, pp. 29–31), T. Kocher looked at the origins of a diverse flock of cichlid fishes in the lakes of southeast Africa. Suppose that you wanted to select a sample from the hundreds of species of cichlid fishes that live in the lakes of southeast Africa. If you took a simple random sample from the species of each lake and combined all the simple random samples into one sample, which type of sampling design would you have used? Explain your answer.

In the article “The Eastern Cottonmouth (Agkistrodon piscivorus) at the Northern Edge of Its Range” (Journal of Herpetology, Vol. 29, No. 3, pp. 391–398), Blem and Blem examined the reproductive characteristics of the eastern cottonmouth, a once widely distributed snake whose numbers have decreased recently due to encroachment by humans. A simple random sample of 44 female cottonmouths yielded a sample mean of ??̅ = 7.6 young per litter. Assume σ = 2.4. a. Is the sample mean likely to equal μ exactly? Explain your answer b. Find the 95% Confidence Interval. c. How large a sample would be needed to get at 99% confidence interval with a margin of error of just 0.1?

The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 52 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are μ=28.29 and σ=33.493, respectively. Let ?X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x¯. Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 52 counties will be less than $29…

Question 7