• In college class with 25 students, 12 of whom are black, the mean on the midterm was 75. The standard deviation was 18. What is the margin of error for this mean?  We use Formula Four because the question is about a mean score.   M = 2 * sd / SQRT(N)   What's N?  N is 25 because the mean score applies to the whole class.    M = 2 * 18/SQRT(25).  36/5 = 7.2 points.

 
• A researcher wants to obtain a margin of error of no more than 3% in a survey of a county with a population of 300,000. How large a sample is needed?  Use formula 3 because the questions is, how large a sample is needed?   N = 1/(M*M).   M means the margin of error expressed as a proportion.  M = .03.     N =1/.03*.03  =    1/.0009.  = 1112.

 
• 65% of the respondents in a survey of a state with seven million Republican voters voted for Gore, 35% for Bush. There were 1625 respondents. What is the margin of error for the percent voting for Bush?  M = 2 * SQRT((p * (1-p))/N).  N = sample size to which the question refers, in this case the whole sample of 1625.  p is the percentage result, expressed as a proportion.  p = .35,  1-p = .65.  p*(1-p)  = .2275/1625.   1.4^E-4.  This is exponential, it means 1.04 * 10^-4 or "move the decimal point four points to the left".  = .0237  or 2.4%

 
• In a survey of 1000 voters, 600 were Democrats, 300 Republicans and 100 Libertarian. 85% of the Republicans favored George W. Bush in the primary. What is the margin of error for this percentage?  M = 2 * SQRT((p * (1-p))/N)  .  N = 300   = .0412 or 4.1%

 
• In a survey of community residents, the mean income was $18,745 with a standard deviation of $1,345. There are 370,000 residents in the community. 1000 were sampled in the survey. What is the margin of error for this mean score?  A mean score question, formula 4  M = 2 * sd / SQRT(N)  sd = 1345   N = 1000.  2 * 1345 = 2690;  SQRT (1000) = 31.62   $85.07  -  What if we sampled only 25 people?  2690/5 = $538.

 
• In a survey of Camden County residents, 85% were in favor of a proposal to abolish traffic circles. There are 300,000 county residents, of whom 200 were sampled. What is the margin of error on this percentage? Formula 2,  p - .85, N = 200,  answer is 5.05%.

 
• A survey of the tri-county area has 356 respondents, of whom 82 are black and 45 Hispanic. What is the margin of error for statistics about the opinion of the Hispanic residents?  Formula One, because no percent is given and no mean score is given.  The tricky question here is, what is N?  N = 45 because the statement is about the Hispanics.   M 1/SQT(45).  = .149 or 14.9%.

 
• What is the margin of error for statistics based on the responses of all the respondents?Same formula, but N = 356.  Result = 5.3%.

 
• In a survey of Rutgers students, 250 white students were sampled and 117 black students. 87% of the students said that Methods and Techniques of Social Research was the most useful class they ever had. What is the margin of error for this percentage? M = 2 * SQRT((p * (1-p))/N)  p = .87, N = 250+117 = 367.  = 3.5%

 
• A study of Rutgers Camden Sociology Department graduates showed that the mean annual salary was $55,000 with a standard deviation of $4500. Three hundred graduates were sampled. What is the margin of error for this statistic?  Formula 4, mean score.  SD 4500, N = 300.  9000/17.32 = $519.62.  Note:  the SD given out in class was different from the one online.