Question

A random sample of 160 households is selected to estimate the mean amount spent on electric service. A 95% confidence interval was determined from the sample results to be ($151, $216). Which of the following is the correct interpretation of this interval?

A We are 95% confident that the mean amount spent on electric service among all households is between $151 and $216.
B There is a 95% chance that the mean amount spent on electric service is between $151 and $216.
C 95% of the households will have an electric bill between $151 and $216.
D We are 95% confident that the mean amount spent on electric service among the 160 households is between $15

Answer 1

Option D. We are 95% confident that the mean amount spent on electric service among the 160 households is between $151 and $216.

Step-by-step explanation:

A confidence interval is a range of values, derived from the sample statistics, which may include the value of an unknown population parameter.

A 95% confidence interval indicates that between 152 of 160 samples (95%) of the same population will produce confidence intervals that will contain the population parameter.

It also means that we have a 95% confidence that the average (average amount) is among the resulting amounts obtained.

Logically, option "D" is missing the final part. This would be: D. We are 95% confident that the mean amount spent on electric service among the 160 households is between $ 15.

This is the only true option, since the test is based on a sample of only 160 households, the entire population of households cannot be included.

Hence, the correct option is:

Option D. We are 95% confident that the mean amount spent on electric service among the 160 households is between $151 and $216.