Question

Video Games: Checking Requirements Twelve different video games showing alcohol use were observed. The duration times of alcohol use were recorded, with the times (seconds) listed below (based on data from “content and rating of Teen-Rated Video Games,” by Haninger and Thompson, journal of the American Medical Association, Vol.291, No.7). What requirements must be satisfied to test the claim that the sample is from a population with a mean greater than 90 sec? Are the requirements all satisfied?

84 14 583 50 0 57 207 43 178 0 2 57

Short answer

The requirements for the given data are the sample should be selected randomly, and the data should be normally distributed (or sample size must be larger than 30).

All the requirements do not satisfy.

Step-by-step solution

Given information

The duration times of alcohol use for 12 different video games were recorded. The population mean$\left(\mu \right)=90\text{sec.}$

State the hypotheses

For the true mean value , the hypothesis is stated as follows:

$$\begin{gathered} H_0:\mu =90(\text{null}\text{hypothesis}) \\ {H}_1:\mu >90(\text{alternative}\text{hypothesis}\text{and}\text{original}\text{claim}) \end{gathered}$$

State the requirements

The following requirements need to be verified for conducting the test:

1. The given sample is selected randomly from the population.
2. The sample size is either larger than 30 or the population is distributed normally.

Check the requirements

The normal Q-Q plot is sketched using the following steps:

1. Draw two axes, horizontal and vertical.
2. Mark z-scores corresponding to the observations on the change by means of scaling the axes.
3. Thus, the relevant graph along with a tentative line is shown below.

The points are not close to the straight line; they deviate. Hence, this is not normally distributed.

Also, the sample is not specified to be selected by random selection.

Thus, the requirements are not satisfied.