You collect a sample from a subpopulation, and based on x-bar, s and n, you calc

Question

You collect a sample from a subpopulation, and based on x-bar, s and n, you calculate a 95% confidence interval for the true mean (). Which statement about that confidence interval is most correct? Please explain thoroughly.

You have 95% confidence that you performed that calculations correctly.

You have 95% confidence that a type I error was made.

With that calculated interval, for every 100 true means of the population, 95 of those true means will fall within that interval.

For every 100 confidence intervals, each created from a different sample group from that population, there will be 95 intervals that will correctly cover the true mean.

You have 95% confidence that you performed that calculations correctly.

You have 95% confidence that a type I error was made.

With that calculated interval, for every 100 true means of the population, 95 of those true means will fall within that interval.

For every 100 confidence intervals, each created from a different sample group from that population, there will be 95 intervals that will correctly cover the true mean.

Explanation / Answer

C

With that calculated interval, for every 100 true means of the population, 95 of those true means will fall within that interval.

We are basically creating a Sampling distribution which has the same mean(mu) as the population and standard deviation (s/n1/2).

According to Central limit theorem (CLT) ,given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population. And all the samples will follow an approximate normal distribution pattern, with all variances being approximately equal to the variance of the population divided by each sample's size.

A 95% Confidence Interval means that if the same population is sampled on numerous occasions and interval estimates are made on each occasion, the resulting intervals would bracket the true population parameter in approximately 95 % of the cases.

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