## The 2003 Statistical Abstract of the United States reported that the percentage of people 18 years of age and older who smoke. Suppose that

Question

The 2003 Statistical Abstract of the United States reported that the percentage of people 18 years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.30. a. [2.5 pts] How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 0.02

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6 months 2021-08-21T22:43:50+00:00 1 Answers 1 views 0

A sample of 2017 should be taken.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is of:

Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.30.

This means that

Confidence level:

Not given, so I will use 95%.

This means that , z is the value of Z that has a pvalue of , so .

a. [2.5 pts] How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of 0.02?

A sample of n should be taken.

n is found fo M = 0.02. So

Rounding up:

A sample of 2017 should be taken.