A study was conducted to determine the average number of words children learn during their third year.For a random sample of one hundred children,parents reported the number of words spoken at 24 months and then again at 36 months of age.A 98% confidence interval for the difference of the means at 36 months and 24 months,μ36 - μ24,was determined to be $( 200,277 ) .$
A)We are 98% confident that,on average,the number of words spoken by children at 36 months of age is between 200 and 277 words greater than the number of words spoken by children at 24 months of age.
B)We know that 98% of children say between 200 and 277 more words at 36 months of age than at 24 months of age.
C)We are 98% confident that the children in this sample said,on average,between 200 and 277 more words at 36 months than at 24 months of age.
D)We know that 98% of all random samples done on the population will show that the average number of words spoken by children is between 200 and 277 words greater at 36 months than at 24 months of age.
E)We are 98% confident that a randomly selected child will say between 200 and 277 more words at 36 months than at 24 months of age.

Question

Quizplus · Accepted Answer

The correct interpretation of a confidence interval is about the population parameter (in this case, the average difference in the number of words spoken between 36 and 24 months of age), not about individual observations or percentages of individuals within a certain range. Therefore, statement A correctly describes the confidence interval's meaning.

A Study Was Conducted to Determine the Average Number of Words