Question

here are summary statistics for randomly selected weights of newbom girls: ( n = 36 ), ( overline{x}=3211.1 mathrm{~g} ), ( s = 689.4 mathrm{~g} ). use a confidence level of ( 90 % ) to complete parts (a) through (d) below. (round to two decimal places as needed.) b. find the margin of error. ( e = 194.2 mathrm{~g} ) (round to one decimal place as needed.) c. find the confidence interval estimate of ( mu ). ( 3016.9 mathrm{~g}<mu<3405.3 mathrm{~g} ) (round to one decimal place as needed.) d. write a brief statement that interprets the confidence interval. choose the correct answer below. a. there is a ( 90 % ) chance that the true value of the population mean weight of newborn girls will fall between the lower bound and the upper bound. b. one has ( 90 % ) confidence that the sample mean weight of newborn girls is equal to the population mean weight of newborn girls. c. one has ( 90 % ) confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls. d. approximately ( 90 % ) of sample mean weights of newborn girls will fall between the lower bound and the upper bound.

Explanation:

A confidence interval is an interval estimate of a population parameter. A 90% confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about 90% of those intervals would contain the true population parameter. Option C correctly interprets this concept as it states that one has 90% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls. Option A is incorrect because it implies a probability that the true value falls within the interval (the true value is a fixed number, not a random variable). Option B is wrong as it compares the sample mean to the population mean (the confidence interval is about the population mean). Option D is incorrect as it refers to sample mean weights instead of the population mean.

Answer:

C. One has 90% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls.