Question

here are summary statistics for randomly selected weights of newborn girls: ( n = 36 ), ( overline{x}=3150.0 g ), ( s = 695.5 g ). use a confidence level of ( 99% ) to complete parts (a) through (d) below.
( 2834.7 g<mu<3465.3 g )
(round to one decimal place as needed.)
d. write a brief statement that interprets the confidence interval. choose the correct answer below.
○ a. one has ( 99% ) confidence that the sample mean weight of newborn girls is equal to the population mean weight of newborn girls.
○ b. approximately ( 99% ) of sample mean weights of newborn girls will fall between the lower bound and the upper bound.
○ c. there is a ( 99% ) chance that the true value of the population mean weight of newborn girls will fall between the lower bound and the upper bound.
○ d. one has ( 99% ) confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls.

Explanation:

A confidence interval gives a range of values within which we are confident the population parameter (here, the population mean weight of newborn girls) lies. A 99% confidence level means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population mean.

• Option A is incorrect because the confidence interval is about the population mean, not stating that the sample mean is equal to the population mean.
• Option B is wrong as it refers to sample mean weights, while the confidence interval is for the population mean.
• Option C is incorrect as it implies a probability (chance) for the population mean being in the interval. The population mean is a fixed value; either it is in the interval (which we don't know for sure) or not. The confidence level refers to the long - run proportion of intervals (from repeated sampling) that contain the population mean.
• Option D is correct as it correctly interprets the 99% confidence interval as having 99% confidence that the interval contains the true population mean.

Answer:

D. One has 99% confidence that the interval from the lower bound to the upper bound contains the true value of the population mean weight of newborn girls.