Flawed Confidence Interval Interpretation
A study compared the mean daily calcium intake, in milligrams (mg), of vegetarian and non-vegetarian adolescents. From independent random samples of 45 vegetarian and 52 non-vegetarian adolescents, a 90 percent confidence interval for the difference in population mean daily calcium intake (non-vegetarian minus vegetarian) was determined to be (-42, 156). Which of the following statements represents a flawed interpretation of this confidence interval?
We are 90% confident that the difference in mean daily calcium intake between the two samples is between -42 mg and 156 mg.
We are 90% confident that the mean daily calcium intake for non-vegetarian adolescents is between 42 mg less and 156 mg more than for vegetarian adolescents in the populations from which these samples were drawn.
We are 90% confident that vegetarian adolescents consume between 42 mg less and 156 mg more calcium daily than non-vegetarian adolescents.
90% of all confidence intervals constructed in this manner will contain the true difference in mean daily calcium intake between the two populations.
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