Question #339921

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


1
Expert's answer
2022-05-13T10:07:07-0400

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

H0:μ=240H_0:\mu=240

Ha:μ240H_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>zc}.R = \{z: |z| >z_c\}.


c)The z-statistic is computed as follows:



z=xˉμσ/n=20024020/5014.1421z=\dfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\dfrac{200-240}{20/\sqrt{50}}\approx-14.1421

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