"A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087...

"A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477(a) Construct a 90 percent confidence interval for the true mean weight. (b) What sample sizewould be necessary to estimate the true weight with an error of ± 0.03 grams with 90 percent confidence?(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls duringmanufacture. (Data are from a project by MBA student Henry Scussel.) TootsieIn 1992, the FAA conducted 86,991 pre-employment drug tests on job applicants who were to be engaged in safety and security-related jobs, and found that 1,143 were positive. (a) Construct a 95 percent confidence interval for the population proportion of positive drug tests. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data are from Flying 120, no. 11 [November 1993], p. 31.)5. State the main points of the Central Limit Theorem for a mean.6. Why is population shape of concern when estimating a mean? What does sample size have to do with it?