Statistics home work problems

1) State the main points of the Central Limit Theorem.

2) Why is the population shape of concern when estimating a mean? What does sample size have to do with it?

3)A random sample of 10 minature 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 3.270 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 size would 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 during manufacture.

4) In 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?