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Q: What percentage of time will the population proportion not be found within the confidence interval?

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You probably mean the confidence interval. When you construct a confidence interval it has a percentage coverage that is based on assumptions about the population distribution. If the population distribution is skewed there is reason to believe that (a) the statistics upon which the interval are based (namely the mean and standard deviation) might well be biased, and (b) the confidence interval will not accurately cover the population value as accurately or symmetrically as expected.

Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.

Why confidence interval is useful

The confidence interval becomes smaller.

if the confidence interval is 24.4 to 38.0 than the average is the exact middle: 31.2, and the margin of error is 6.8

Related questions

There is a 95% probability that the true population proportion lies within the confidence interval.

Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.

You probably mean the confidence interval. When you construct a confidence interval it has a percentage coverage that is based on assumptions about the population distribution. If the population distribution is skewed there is reason to believe that (a) the statistics upon which the interval are based (namely the mean and standard deviation) might well be biased, and (b) the confidence interval will not accurately cover the population value as accurately or symmetrically as expected.

A confidence interval of x% is an interval such that there is an x% probability that the true population mean lies within the interval.

The Confidence Interval is a particular type of measurement that estimates a population's parameter. Usually, a confidence interval correlates with a percentage. The certain percentage represents how many of the same type of sample will include the true mean. Therefore, we would be a certain percent confident that the interval contains the true mean.

Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.

The confidence interval for this problem can be calculated using the following formula: Confidence Interval = p ± z*√(p*(1-p)/n) Where: p = observed proportion (54%) n = sample size (80) z = z-score (1.96) Confidence Interval = 0.54 ± 1.96*√(0.54*(1-0.54)/80) Confidence Interval = 0.54 ± 0.07 Therefore, the confidence interval is 0.47 - 0.61, meaning that we can be 95% confident that the percentage of voters who prefer the referred candidate is between 47% and 61%.

confidence interval estimate

Why confidence interval is useful

, the desired probabilistic level at which the obtained interval will contain the population parameter.

No. For instance, when you calculate a 95% confidence interval for a parameter this should be taken to mean that, if you were to repeat the entire procedure of sampling from the population and calculating the confidence interval many times then the collection of confidence intervals would include the given parameter 95% of the time. And sometimes the confidence intervals would not include the given parameter.

The confidence interval becomes wider.

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