A sample of 3,014 steelworkers was selected to find out if they will go on strike on Monday. 53.2% of those in the sample said they would go out on strike. Since the number sampled is large and those advocating a strike constitute over 50%, can we assume that the majority of all steelworkers favor a strike? (assume the sample is large enough and random and representative)
I would personally disagree with the above answer. The questions is stating that we ARE to assume that the sample is large enough, random and representative. The whole point of taking a sample is that if it is randomly selected and representative of the whole population, the results can be then potentially extrapolated to the entire population. In this particular case it would be helpful to know the confidence interval and margin of error to be completely sure that we could then extend these results to the population. I couldn't say for sure that we can assume that the majority of all steelworkers favor a strike, but this is only because I do not know the confidence interval and margin of error.
This website is useful for explaining some of these topics. http://www.edrm.net/projects/search/statistical-sampling/estimating
Nice hearing from you, Nashonda!
Your inquiry reminds me of a problem once posed by Abraham Lincoln:
"If you call a tail a 'leg', how many 'legs' does a dog have?"
Answer: FOUR legs -- calling a tail a "leg" does NOT MAKE it a "leg."
Your teacher may not like my answer, Nashonda, but "assuming a 'large ... representative' sample" does NOT make it so ... it has to be shown. Here's an excerpt from my profile's "Statistics" subject description:
Statistics hopes that samples look like whole populations. The sample is described by a typical, central value: an average, mean, or median. The sample also has a "spread" or range about the average: a standard deviation. Normally, about two-thirds of the group will lie within one standard deviation of the average, and about 95% lives within two standard deviations. Is the sample size big enough? I prefer sampling until there's not much change in medians. Then I over-sample to be sure.
Wishing you the very best in your studies, ma'am :)