Which set of characteristics will produce the smallest value for the estimated standard error? Group of answer choices a large sample size and a large sample variance a small sample size and a small sample variance a large sample size and a small sample variance a small sample size and a large sample variance

Question

Physics

Duke

4 March, 00:03

Which set of characteristics will produce the smallest value for the estimated standard error? Group of answer choices a large sample size and a large sample variance a small sample size and a small sample variance a large sample size and a small sample variance a small sample size and a large sample variance

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Answers (1)

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Essence Hull · Answer 1

a large sample size and a small sample variance

Explanation:

If the confidence interval is too wide, you cannot be very sure of the actual value of a parameter, such as the average. However, you can use several strategies to reduce the width of a confidence interval and make the estimate more accurate and therefore decrease the standard error. The following features affect the width of the confidence interval.

- Sample size

- Variation in the data

- Type of interval

- Confidence level

Increase sample size

Frequently, the most practical way to reduce the margin of error is to increase the sample size. In general, the more observations there are, the narrower the interval around the sample statistic will be. Therefore, it is recommended to collect more data to obtain a more accurate estimate of a population parameter.

You should weigh the benefits of greater accuracy with respect to the time and additional resources needed to collect a larger sample. For example, a confidence interval that is narrow enough to contain only the population parameter requires that all subjects in the population be measured. Obviously, this strategy would usually be very impractical.

Reduce variability

The less the data varies, the more accurate the estimate of a population parameter will be.

This is due to the fact that when the variability of the data is reduced, the standard deviation decreases and, therefore, the margin of error of the estimate. Although it can be difficult to reduce the variability of the data, it can sometimes be achieved by adjusting the way in which the data is collected. For example, you can use a paired design to compare two groups. It could also reduce variability by improving the process, so that the process is more consistent, or measuring more accurately.