The chamber of commerce in a beach resort town wants to estimate the proportion
ID: 3151160 • Letter: T
Question
The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors. Suppose that they have estimated that they need a sample size of n=16,577 people to achieve a margin of error of ± .01 percentage points with 99 percent confidence, but this is too large a sample size to be practical. How can they reduce the sample size?
Use a higher level of confidence
Use a smaller margin or error
Use a lower level of confidence
Conduct a census
Use a higher level of confidence
Use a smaller margin or error
Use a lower level of confidence
Conduct a census
Explanation / Answer
As we increase the confidence level of our estimates—from 95 to 99, for example—our confidence interval gets larger. In other words, in order to be more confident that our interval actually contains the population mean, we have to increase the size of the interval, i.e., we have to be less precise. How can we mitigate that tradeoff between level of confidence and the precision of our interval? We do this primarily by increasing our sample size.
Larger samples result in smaller standard errors, and therefore, in sampling distributions that are more clustered around the population mean. A more closely clustered sampling distribution indicates that our confidence intervals will be narrower and more precise
As the sample size increases, the interval and its width decrease, thus providing a more precise estimate of the population value.
Answer- B and C
Use a lower level of confidence
,
Use a lower level of confidence
,
Use a lower level of confidence
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