Suppose the weights of seventh-graders at a certain school vary according to a Normal distribution, with a mean of 100 pounds What would the \( P \)-value tell the researcher in this situation? the probability that a random sample of students would have a mean less than or equal to 98 pounds, if the true population mean is 100 pounds the probability that a rand lunch program at the school. She finds, in a random sample of 35 students, an average weight of 98 pounds. 100 pounds the probability that a random sample of students would have a mean of 98 pounds, if the true population mean is a mean of 100 pounds, if the true population mean is 98 pounds the probability that a random sample of students would have a mean less than orequal to 100 pounds, if the true population mean is 98 pounds

In the context of hypothesis testing, the \( P \)-value is a measure that helps researchers determine the strength of the evidence against the null hypothesis. In this case, the null hypothesis (\( H_0 \)) could be that the true population mean weight of seventh-graders is 100 pounds. Given the options you provided, the correct interpretation of the \( P \)-value in this situation would be: **The probability that a random sample of students would have a mean less than or equal to 98 pounds, if the true population mean is 100 pounds.** This interpretation aligns with the typical use of the \( P \)-value in hypothesis testing, where you assess how likely it is to observe a sample mean (or more extreme) under the assumption that the null hypothesis is true. If the \( P \)-value is low, it suggests that observing a sample mean of 98 pounds (or lower) is unlikely if the true mean is indeed 100 pounds, which could lead to rejecting the null hypothesis in favor of an alternative hypothesis (e.g., that the true mean is less than 100 pounds).