Population in the News
An article by Tackett, M. (2012) is analysed in this paper. The Bloomberg news article is dated 22nd June 2012 and discusses a presidential poll survey result. The article reports the results of three different surveys, which include a survey by Pew research centre, Bloomberg polls and associated press polls. The article reports the sample mean values, the margin of error and confidence intervals for the estimated mean values. (Tackett, 2012)
The results of Bloomberg survey indicated that the average difference in rating between Obama and Romney was 13 point in favour of Obama, Associated press survey indicated the average difference in rating was 3 points in favour of Obama and finally the Pew survey indicated that the average difference in rating was 4 points in favour of Obama. Bloomberg polls survey sample size was 1,002 and the margin of error was 3.1 percent with a 95% confidence interval. The Associated press survey sample size was 1,007 and the margin of error was 4 percent, finally the Pew survey sample was 2,013 and the margin of error was 2.5 percent (Tackett, 2012).
The margin of error clearly shows the error associated with a sample in estimating the population mean, the higher the value of the margin of error then the error associated with the estimation of the population mean. The margin of error is used in estimating the required sample size, the lower the margin of error example 2%, then the larger the required sample size example in this case the sample size would be 2000. When the margin of error is higher example 10%, then the smaller the required sample size example in this case the sample size would be 400.
Confidence interval is also used in estimating the sample size required, for example 95%, 98% and 99%. The higher the confidence interval, then the higher the required sample size, a 95% confidence interval will require a larger sample compared to a 99% confidence interval. The three surveys discussed above indicates this trend, given that the three surveys have a margin of error of 3.1%, 4% and 2.5% for Bloomberg, Associated press and Pew survey respectively. In addition, the sample size was 1,002, 1,007 and 2,013 for Bloomberg, Associated press and Pew survey respectively. Results indicate that Pew survey has a lower margin of error and therefore the sample size is larger (Bennett, Briggs and Triola, 2009, pp 5).
Comparing the Bloomberg and associated press survey sample size, it is evident that the sample sizes are almost equal at 1,002 and 1,007. The margin of error is 3.1% and 4% for Bloomberg and associated press survey respectively. This shows that there is a difference in the confidence interval, the Bloomberg survey confidence interval is 95% and this means that the associated press survey entailed having a higher confidence interval (Bennett, Briggs and Triola, 2009, pp 5).
The confidence interval and margin of error also explain the reliability of results in each survey results, the Bloomberg margin of error is 3.1% and the confidence interval is 95%. This means that there is a 95% confidence that the estimated average rating is plus or minus 3.1%, these values also means that there is a 5% probability that the estimated average rating is above plus or minus 3.1% (Bennett, Briggs and Triola, 2009, pp 5).
The Pew survey results are more reliable due to the lower margin of error, the estimated average rating is a more accurate estimate of the population mean, this is due to the fact that the estimated average rating is plus of minus 2.5% of the estimated value. Associated press results are less reliable due to the fact that the margin of error is the highest at 4% (Bennett, Briggs and Triola, 2009, pp 6).
Reference:
Bennett, J., Briggs, W. and Triola, M. (2009). Statistical Reasoning for everyday life. (3rd Ed.).New York: Addison-Wesley Longman.
Tackett, M. (2012). Obama Lead Varies in 3 Polls. Retrieved on 17th September, available at http://www.bloomberg.com/news/2012-06-22/obama-lead-varies-in-3-polls-with-no-one-declaring-which-is-best.html
