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Q: Why confidence interval useful?

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The confidence interval becomes wider.

how are alpha and confidence interval related

No. The width of the confidence interval depends on the confidence level. The width of the confidence interval increases as the degree of confidence demanded from the statistical test increases.

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.

The confidence interval is not directly related to the mean.

The confidence interval becomes smaller.

no,these are not the same thing.The values at each end of the interval are called the confidence limits.

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 width of the confidence interval increases.

No, it is not. A 99% confidence interval would be wider. Best regards, NS

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confidence level

Generally speaking an x% confidence interval has a margin of error of (100-x)%.

Narrow because there is less of a chance for people to mess up

That, my friend, is not a question.

The Z-value for a one-sided 91% confidence interval is 1.34

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

An open interval centered about the point estimate, .

The confidence interval consists of a central value and a margin of error around that value. If it is an X% confidence interval then there is a X% probability that the true value of the statistic in question lies inside the interval. Another way of looking at it is that if you took repeated samples and calculated the test statistic each time, you should expect X% of the test statistics to fall within the confidence interval.

Confidence level 99%, and alpha = 1%.

True.

The width reduces.

2.4299999999999997

The standard deviation is used in the numerator of the margin of error calculation. As the standard deviation increases, the margin of error increases; therefore the confidence interval width increases. So, the confidence interval gets wider.

Statistical estimates cannot be exact: there is a degree of uncertainty associated with any statistical estimate. A confidence interval is a range such that the estimated value belongs to the confidence interval with the stated probability.