You learn that the confidence interval at the 95% level for the variable AGE in

Question

You learn that the confidence interval at the 95% level for the variable AGE in the General Social Survey is 45.52 at the lower limit and 47.28 at the upper limit. The mean for the variable is 46.40. Which of the following statements best interprets the confidence interval?

A.)There are 95 chances out of 100 that the true population mean is either 45.52 or 47.28.

B.)There are 95 chances out of 100 that the range of ages between 45.52 and 47.28 contains the population mean for the age of American adults.

C.)95% of all of the respondents are between the ages of 45.52 and 47.28.

D.) 95% of all Americans are between the ages of 45.52 and 47.28.

Explanation / Answer

B is correct.

A confidence interval is always about the population parameter, and therefore, A is wrong. It is a range inside which the poulation parameters exists with certain chance

B is the correct interpretation. The confidence interval is interpreted as " there is a X% chance that the true population mean lies between a range".

C, D are out, because the confidence interval is about population ( not all respondents or all Americans)>

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