Answer to Question #340897 in Statistics and Probability for Hanna

Question

A study claims tha.t on average, male high school students spend at least 3.39 hours a day playing video games with a standard deviation of 2.05 hours. A random sample of 30 teenagers were surveyed and the results showed that these teenagers spend 4.12 hours a day playing video games.

Solve for the z-score of the sample mean of 4.12 hours

Answer 1

The z-score of the sample mean is

$$z=\dfrac{\bar{X}-\mu}{s/\sqrt{n}}=\dfrac{4.12-3.39}{2.05/\sqrt{30}}\approx1.9504$$