A survey of 811 registered voters in Florida, taken at the end of September 1994

Question

A survey of 811 registered voters in Florida, taken at the end of September 1994, reported that 57% of the respondents are against legalized casino gambling in Florida. The article reporting the survey states that the sampling error is 3.5%. a. Is this the correct sampling error to report? b. Can a valid statistical argument be made that "most Floridians disapproved of legalizing casinos in the state at that time?" Explain. c. Proponents of the casinos say that their poll shows only a little over one-third of the people in the state opposed casinos. What could cause this difference between the two poll results?

Explanation / Answer

Sampling error is caused due to sample study. As population size is quite large, it is impracticable to study each & every unit of population , so we study sample units which is a part of the population.Most important part is that sample should be unbised, proportional to the population size , then only sample can become a good representative of the population to get correct results as well to reduce sampling error as we are going to apply sample results on population. Here we have taken a survey of only 811 registered voters, again it may happen that some of the voteres have not tegistered at the time of survey & some may be below age. As a result , population size becomes quite large as compared to sample size which is not the true representative of the population Hence sample results which we have obtained can not be considered as the conclusion for the population. Here it seems that 57% of respondents are against casino gambling ( some may be nonrespondents also out of 811) which can not be related to the population as the sample size is quite small compared to the population size. a) so it can not be the correct sampling error to report. b) " most floridians disapproved legalising casinoes in the state at the time " This statement is made about the population which is invalid as here sample size is not proportional to the population size. c) Proponents of the casinoes poll showed only alittle difference. But state poll showed quite large difference ie 57 : 43. These differences between two polls are caused just because of the sample size differences. That is state population size is quite large as compared to the population of the proponents of the casinoes. Again this may be caused due to the differences in the sampling techniques

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