Question
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.
Ask by Rowe Rowe. in the United States
Nov 24,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
我们95%确信，过去一年中至少作弊两次的高中生比例在34%到35%之间。
Solution
根据全国高中生调查，40,774名学生中有14,028名学生表示在过去一年中至少作弊两次。对于这个参数的95%置信区间是（0.34，0.35）。假设满足推断的条件和假设。
选择这个区间的正确解释：
我们95%确信，在过去一年中至少作弊两次的高中生比例在34%到35%之间。
我们95%确信，所有随机抽取的高中生样本都会报告作弊率在34%到35%之间。
我们知道95%的样本表示他们作弊的比例在34%到35%之间。
信息不足，我们需要P值。
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Beyond the Answer
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!
