Question

After teaching confidence interval in your Statistics class, you came across a recent poll that reports that a 95% confidence interval for the mean ideal weight for adult American women is 139 ± 1.4 pounds. When you asked your students to explain the meaning of this confidence interval, two students said the following: Student #1: “95% of all adult American women would say that their ideal weight is between 137.6 and 140.4 pounds.” Student #2: “We can be 95% confident that future samples of adult American women will say their mean ideal weight is between 137.6 and 140.4 pounds.” Discuss what you think about the explanations of the two students. Are they correct? Explain.

Answer 1

Sol:

lower limit=139-1.4= 137.6

upper limit=139+1.4=140.4

confidence interval gives parameter estimates,here population mean

if we take random samples and estimate the popualtion mean ,in 95% of the times we get the popualtion mean lying in between 137.6 and 140.4

In 5% of the times we dont get the population mean lying in the interval (137.6,140.4)

Intrepretation;

we are 95% confident that the true mean  ideal weight for all adult American women lie ion between 137.6 and 140.4 .

Both the students are wrong