15-06-2018
Mathematics

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A study of one thousand teens found that the number of hours they spend on social networking sites each week is normally distributed with a mean of 10 hours. The population standard deviation is 2 hours. What is the 95% confidence interval for the mean?

A) 9.88−10 hours
B) 10−10.12 hours
C) 9.88−10.12 hours
D) 9.76−10.24 hours

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15-06-2018

The answer is letter C - 9.88-10.12 hours.

A two-tailed 95% confidence interval is z = +/- 1.96. Then the bounds of the confidence interval can be determined as:Lower bound = mean - z*SD/sqrt(n) = 10 - 1.96*2/sqrt(100) = 10 - 0.1240 = 9.8760 hoursUpper bound = mean + z*SD/sqrt(n) = 10 + 1.96*2/sqrt(100) = 10 + 0.1240 = 10.1240 hours

So the third choice is the correct answer: 9.88-10.12 hours

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