Answer to Question #339921 in Statistics and Probability for None

Question

A researcher is conducting a study on the average time consumed by HS students in playing mobile games. A sample of 50 HS students has an average of 200 minutes. Test the null hypothesis that the average time consumed by students is 240 minutes with a population standard deviation of 20.

a) formulate the null and alternative hypothesis

b) determine what test statistic to use

c) calculate the test statistic value

Answer 1

a) The following null and alternative hypotheses need to be tested:

$H_0:\mu=240$

$H_a:\mu\not=240$

b)This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

The rejection region for the two-tailed test is $R = \{z: |z| >z_c\}.$

c)The z-statistic is computed as follows:

$$z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{200-240}{20/\sqrt{50}}\approx-14.1421$$