(Solved): A sample of 14 plants was taken and the mean height was \( 21 \mathrm{~cm} \). A \( 95 \% \) confid ...

A sample of 14 plants was taken and the mean height was \( 21 \mathrm{~cm} \). A \( 95 \% \) confidence interval for the true mean height of plants of that particular species is \( (17.6 \mathrm{~cm}, 24.4 \mathrm{~cm}) \). Four students gave the following interpretations of the confidence interval. Which of the following is correct? We are \( 95 \% \) confident that the true mean height is \( 21 \mathrm{~cm} \) since that value lies in the confidence interval. We can be fairly confident that \( 95 \% \) of all plants of that species have a height between \( 17.6 \mathrm{~cm} \) and \( 24.4 \mathrm{~cm} \). The probability is \( 0.95 \) that the mean height lies in the interval \( (17.6,24.4) \). We are \( 95 \% \) confident that the true mean height for all plants of that species will lie in the interval \( (17.6,24.4) \)