Explaining confidence. A student reads that a 95% confidence interval for the mean ideal weight given by adult American women is 140 ± 1.4 pounds. Asked to explain the meaning of this interval, the student says, “95% of all adult American women would say that their ideal weight is between 138.6 and 141.4 pounds.” Is the student right? Explain your answer.
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We have a population of all adult women. We take a random sample from this population and create a confidence interval. If we take many, many, many different samples from this population we will obtain many, many, many different sample means and confidence intervals created using the data from our samples. If we created many, many, many different confidence intervals in this manner 95% of them would capture the true mean weight of the population of all women.
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