Answer to Question #311149 in Statistics and Probability for john

Question

The average time spent in a week by grade 11 students browsing their favorite social networking sites is 12 hours with a standard deviation of 3 hours. If a random sampling of 40 students is selected, find the mean, variance, and standard error of the distribution of all sample means that can be derived from the sample.

Answer 1

Mean of the sampling means is equal to the population mean, so a = 12 hours

Variance: $S^2={\frac V n}={\frac {3^2} {40}}={\frac 9 {40}}$

Standard deviation: $S=\sqrt{{\frac 9 {40}}}={\frac {3\sqrt{10}} {20}}$

standard error: $SE={\frac S {\sqrt {40}}}={\frac 3 {40}}$