According to a 2011 report by the United States Department of Labor, civilian Am

Question

According to a 2011 report by the United States Department of Labor, civilian Americans spend 2.75 hours per day watching television. A faculty researcher, Dr. Sameer, at California Polytechnic State University (Cal Poly) conducts a study to see whether a different average applies to Cal Poly students. Suppose that for a random sample of 100 Cal Poly students, the mean and standard deviation of hours per day spent watching TV turns out to be 3.01 and 1.97 hours, respectively. The data were used to find a 95% confidence interval: (2.619, 3.401) hours/day. Which of the following are INVALID interpretations of the 95% confidence interval? Select all that apply.                                             

A

Option A : About 95% of all Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.

B

Option B : There is a 95% chance that, on average, Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.

C

Option C : We are 95% confident that, on average, these 100 Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.

D

Option D : In the long run, 95% of the sample means will be between 2.619 and 3.401 hours.

E                                          

Option E : None of the above.

Explanation / Answer

We have,

95% confidence interval for mean is : ( 2.619 , 3.401 ).

The given confidence interval is for mean ( average) , not for single random variable. Therefore, 95% chance that sample mean is in between 2.619 and 3.401.

Therefore, INVALID  interpretations of the 95% confidence interval is :

Answer : Option A : About 95% of all Cal Poly students spend between 2.619 and 3.401 hours/day watching TV.

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