Question

17. The City of Philadelphia hired a survey firm to measure how many Philadelphians smoke tobacco. The survey firm randomly sampled 1,000 adults who live in Philadelphia and asked them whether they smoked tobacco products or not. The firm coded people who said they smoked tobacco as a 1 and those who said they did not as a 0. Imagine that you are an employee for the survey firm and the task falls to you to analyze these data and explain it to the Mayor of Philadelphia. When you look at the data you find 224 people are coded as tobacco smokers. For this question do the following:

a. Calculate the standard error.

b. Write how you would explain to the Mayor what these data tell us about the percent of Philadelphians who smoke tobacco AND what the standard error tells us.

Answer 1

a.

Sample proportion, = 224/1000 = 0.224

Standard error =

b.

average percent of smokers = 0.224 * 100 = 22.4%

Standard error in percentage = 0.01318423 * 100 = 1.32 %

For 95% confidence interval, z = 1.96

Margin of error = 1.96 * 1.32 = 2.58 %

The standard error of 1.32% is a measure of deviation of sample proportion from the true population proportion.

The average percent of Philadelphians who smoke tobacco is 22.4% with standard deviation of 1.32%. We are 95% confident that average percent of Philadelphians who smoke tobacco is between 22.4 2.58 %.