nina would like to estimate the difference in the mean amount of time students spend on math homework at her…

nina would like to estimate the difference in the mean amount of time students spend on math homework at her public school versus her cousin sharons private school. to do so, each girl selects a random sample of 30 students from their large schools and asks the selected students how much time they spent doing math homework the previous night. nina and sharon would like to construct a 90% confidence interval for the true difference in the population means. are the conditions for inference met?\nyes, all three conditions for inference are met.\nno, the random condition is not met for both samples.\nno, the 10% condition is not met for both samples.\nno, the normal/large sample condition is not met for both samples.

nina would like to estimate the difference in the mean amount of time students spend on math homework at her public school versus her cousin sharons private school. to do so, each girl selects a random sample of 30 students from their large schools and asks the selected students how much time they spent doing math homework the previous night. nina and sharon would like to construct a 90% confidence interval for the true difference in the population means. are the conditions for inference met?\nyes, all three conditions for inference are met.\nno, the random condition is not met for both samples.\nno, the 10% condition is not met for both samples.\nno, the normal/large sample condition is not met for both samples.

Answer

Explanation:

Step1: Check random condition

Each girl selects a random sample of 30 students, so the random condition is met.

Step2: Check 10% condition

The schools are large. A sample of 30 students is likely less than 10% of the population of students in each large - school, so the 10% condition is met.

Step3: Check Normal/Large sample condition

Since (n_1 = n_2=30) (where (n_1) and (n_2) are the sample sizes), by the Central Limit Theorem, for sample sizes (n\geq30), the sampling distribution of the difference in sample means is approximately normal. So the Normal/Large sample condition is met.

Answer:

Yes, all three conditions for inference are met.