In a national survey of high school students, 14,028 of 40,774 students reported that they had cheated at least two times in the last year. A \( 95 \% \) confidence interval for the parameter was determined to be \( (0.34,0.35) \). Assume that the conditions and assumptions for inference are satisfied. Choose the correct interpretation of this interval. We are \( 95 \% \) confident that the proportion of high school students who have cheated at least twice in the last year is between \( 34 \% \) and \( 35 \% \). We are \( 95 \% \) confident that all random samples of high schools students would report a mean cheating rate of between \( 34 \% \) and \( 35 \% \). We know that \( 95 \% \) of the sample said they had cheated between \( 34 \% \) and \( 35 \% \) of the time. There is not enough information; we need a P-value.
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We are \( 95 \% \) confident that the proportion of high school students who have cheated at least twice in the last year is between \( 34 \% \) and \( 35 \% \). This interval provides a range in which we believe the true proportion of all high school students falls, based on our sample data. The confidence interval reflects the variability and uncertainty in our sample estimates, meaning that if we were to conduct this study multiple times, about \( 95 \% \) of those resulting intervals would capture the true proportion of high school students who tend to cheat at least twice annually. So, we can be quite assured that the truth lies snugly within these bounds!
