Question

18 multiple choice 4 points
interpret the confidence interval.
an experiment was conducted to estimate the average fat content of a quarter pounder with cheese. a random sample of 30 burgers produced a sample mean of 26 grams which resulted in a 95% confidence interval of (25, 27) grams.
which of the following is the correct interpretation of this interval?
95% of the quarter pounders with cheese sampled had a fat content between 25 and 27 grams.
we are 95% confident that the mean fat content of the sampled quarter pounders with cheese is between 25 and 27 grams.
we are 95% confident that the mean fat content of a quarter pounder with cheese is between 25 and 27 grams.
we are 95% confident that the range of fat content of a quarter pounder with cheese is between 25 and 27 grams.

Explanation:

A confidence interval estimates the population parameter. Here, the population is all quarter - pounders with cheese. The sample mean is 26 grams (already known for the sample). A 95% confidence interval means that if we were to take many samples and construct confidence intervals, about 95% of them would contain the True population mean.

The first option is wrong because it refers to the sample (not the population mean). The second option is wrong as it refers to the sampled (already known sample mean). The fourth option is wrong as it refers to the range (confidence interval is for the mean).

Answer:

We are 95% confident that the mean fat content of a quarter pounder with cheese is between 25 and 27 grams.