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.​
Suppose that the data had actually been collected from a sample of 150 students, and not 100, but everything else (mean and SD) was the same as reported earlier. How, if at all, would the new 95% confidence interval based on these data differ from the interval mentioned earlier: (2.619, 3.401) hours?

a. The new interval would still be (2.619, 3.401) hours, because we are still 95% confident.

b	The new interval would be narrower than (2.619, 3.401) hours, because the sample size is bigger.

c	The new interval would be wider than (2.619, 3.401) hours, because the sample size is bigger.

d	More information is needed to answer this question.

Answer 1

Given that, 95% confidence interval for population mean with sample size of 100 is, ( 2.619, 3.401 )

Confidence interval formula is,

Where, E is the margin of error.

If we use sample of size 150 then the margin of error decreases and confidence interval becomes narrower.

Therefore,

Answer: b) The new interval would be narrower than (2.619, 3.401) hours, because the sample size is bigger.