What is meant by the term “90% confident” when constructing a confidence interva

Question

What is meant by the term “90% confident” when constructing a confidence interval for a mean?

a. If we took repeated samples, approximately 90% of the samples would produce the same confidence interval.

b. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the sample mean.

c. If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

d. If we took repeated samples, the sample mean would equal the population mean in approximately 90% of the samples.

Explanation / Answer

The correct option is (C) If we took repeated samples, approximately 90% of the confidence intervals calculated from those samples would contain the true value of the population mean.

Note:- Confidence intervals consist of a range of values (interval) that act as good estimates of the unknown population parameter. However, the interval computed from a particular sample does not necessarily include the true value of the parameter. When we say, "we are 90% confident that the true value of the parameter is in our confidence interval", we express that 90% of the hypothetically observed confidence intervals will hold the true value of the parameter. After any particular sample is taken, the population parameter is either in the interval or not. Since the observed data are random samples from the true population, the confidence interval obtained from the data is also random. The 90% confidence level means that 90% of the intervals obtained from such samples will contain the true parameter.

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