A 95% confidence interval contains 5. If the confidence level is increased to 99%, will the...

A 95% confidence interval contains 5. If the confidence level is increased to 99%, will the new interval contain 5?

		Yes
		No
		Unable to determine

Solutions

Expert Solution

The correct option is: Yes [ANSWER]

Explanation:
For the same data, if we construct two confidence intervals at two different confidence levels, then all the points containted in the confidence interval with lower confidence level are also contained in the confidence interval with the higher confidence level.

This is because, for the same set of data, as we increase the confidence level, the confidence interval 'expands' from both sides. This is because as we increase the confidence level we are in effect increasing the probability that confidence interval 'captures' the true value of the parameter, which is achieved by expanding the confidence interval.

Thus, a confidence interval with lower confidence level is in fact a subset of the confidence interval with higher confidence.

[Note that this is true only if it is applied to the same data]

Thus, a point that lies in the 95% confidence interval will also lie in the 99% confidence interval.

Thus, if a 95% confidence interval contains 5, then if the confidence level is increased to 99%, the new interval will also contain 5.

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orchestra answered 1 year ago

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