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A random sample survey of 2,000 motorists found that 827 or 41.4% of them had been to their service garage for repairs and for servicing during the previous three months. What is the standard error of this proportion? (b) Now calculate the standard error of the proportion for samples of 1,000, 4,000 and 8,000 in the above example. What is the relationship between sample size and standard error of the mean and what are the implications of this?

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