Question

A )When pollsters take a random sample of about 1000 people to estimate the mean of some quantity over a population of millions of people, how is it possible for them to estimate the accuracy of the sample mean?

B) Under what conditions, if any, is it not correct to assume that the sampling distribution of the sample mean is approximately normally distributed? Explain your reasoning.

C)Suppose that you want to know the opinions of American secondary school teachers about establishing a national test for high school graduation. You obtain a list of the members of the National Education Association (the largest teachers’ union) and mail a questionnaire to 3000 teachers chosen at random from this list. In all, 823 teachers return the questionnaire. Identify the relevant population. Do you believe there is a good possibility of non-sampling error? Why or why not?

Answer 1

(A)

The concept used here are confidence intervals. A confidence interval of a point estimate (mean, proportion or standard deviation) gives a range of values withing which the true population parameter will lie in.

The confidence interval is found by using the equation point estimate ME, where ME is the margin of error. This error allows for errors in samplings, calculation or other factors. The ME is found by the equation Critical * SE, where critical value is the value for a certain level of confidence with which we are certain the the true population parameter lies in the interval.

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