The authors of a paper on perceptions of video games carried out an experiment to determine if restrictive labels on video games actually increased the attractiveness of the game for young game players. Participants read a description of a new video game and were asked how much they wanted to play the game. The description also included an age rating. Some participants read the description with an age-restrictive label of 7+, indicating that the game was not appropriate for children under the age of 7. Others read the same description, but with an age-restrictive label of 12+, 16+, or 18+. The following data for 12- to 13-year-old boys are consistent with summary statistics given in the paper. (The sample sizes in the actual experiment were larger.) For purposes of this exercise, you can assume that the boys were assigned at random to one of the four age label treatments (7+, 12+, 16+, and 18+). Data shown are the boys' ratings of how much they wanted to play the game on a scale of 1 to 10. 7+ label 7 7 6 5 6 8 6 1 2 4 12+ label 8 7 9 5 7 9 5 8 4 7 16+ label 7 9 8 6 7 5 8 9 6 7 18+ label 10 9 6 9 7 6 8 9 10 8 Find the test statistic and P-value. ( Round your test statistic to two decimal places and your P-value to three decimal places.) F= P-value=
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
7+ label | 7 | 7 | 6 | 5 | 6 | 8 | 6 | 1 | 2 | 4 |
---|---|---|---|---|---|---|---|---|---|---|
12+ label | 8 | 7 | 9 | 5 | 7 | 9 | 5 | 8 | 4 | 7 |
16+ label | 7 | 9 | 8 | 6 | 7 | 5 | 8 | 9 | 6 | 7 |
18+ label | 10 | 9 | 6 | 9 | 7 | 6 | 8 | 9 | 10 | 8 |
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