Question

Thinking of the many variables tracked by hospitals and doctors' offices, confidence intervals could be created for many of them. What variable might be most helpful in your work to be able to create an interval within which 95% of patients would fall? What would limit the ability to create such an interval?

Answer 1

Answer:

The particular value select as most likely for a population limit is called the point estimate. since of sampling error, we know the point estimation possibly is not the same to the population limit. The accuracy of a point estimator depends on the characteristics of the sampling distribution of that estimator.

If, for example, the sampling distribution is roughly normal, then by means of high probability (about .95) the point estimate falls within 2 standard error of the parameter.

since the end estimation is improbable to be accurately correct, we usually specify a range of values in which the population parameter is likely to be. For example, when X is normally distributed, the range of values between X ±1.96? is called the 95% confidence interval for µ.

The two margins of the interval, X X ?1.96? and X X +1.96? are called the 95% confidence limits. That is, there is a 95% chance that the following declaration will we true: X ?1.96? ? µ ? X +1.96? Similarly, when X is normally distributed, the 99% confidence interval for the mean is X ? 2.58? ? µ ? X + 2.58? The 99% confidence interval is larger than the 95% confidence interval, and thus is more likely to include the true mean. ? = the probability a confidence interval will not include the population parameter, 1 - ? = the probability the population limit will be in the interval.

The 100(1 - ?)% confidence interval will include the true value of the population limit with probability 1 - ?, i.e., if ? = .05, the probability is about .95 that the 95% confidence interval will include the true population limit.

On the other hand, 2.5% of the time the highest value in the confidence interval will be smaller than the true value, while 2.5% of the time the smallest value in the confidence interval will be greater than the true value.

Be sure to note that the population parameter is not a random variable. Rather, the probability statement is made about samples.

If we draw 100 sample of the similar size, we would acquire 100 dissimilar example means and 100 dissimilar confidence interval.

We wait for that in 95 of persons sample the population limit will lie within the estimated 95% confidence interval, in the other 5 the 95% confidence interval will not include the true value of the population limit.

Confidence Intervals - Page 1 Of course, X is not always normally distributed, but this is usually not a concern so long as N $ 30. More importantly, ? is not always known. Therefore, how we construct confidence intervals will depend on the type of information and data available.