Answer to Question #350161 in Statistics and Probability for joy

Question

In a certain school, grade 11 students spend an average 14 hours, with a standard duration of 4 hours, in browsing their favorite social networking sites. The average time spent in a week by grade 11 students browsing their favorite social networking sites is 14 hours with a standard deviation of 4 hours. If a random sample of 35 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

$$\mu_{\bar{X}}=\mu=14\ hours$$

$$\sigma_{\bar{X}}^2=\sigma^2/n=\dfrac{16}{35}\ {hours}^2$$

$$SE=\sqrt{\sigma_{\bar{X}}^2}=\sigma/\sqrt{n}=\dfrac{4}{\sqrt{35}}\ {hours}$$

$$\approx0.6761\ hours$$