Question

1. -129 points My Notes The authors of a paper titled "Age and Violent Content Labels Make Video Games Forbidden Fruits for Youth" 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 summary data shown below are the ratings of 12- to 13-year-old boys for how much they wanted to play the game on a scale of 1 to 10. You can assume that boys were assigned at random to one of the four age label treatments(7+, 12+, 16+, 18+) and that ratings were normally distributed Sample Size Group 18+ label 16+ label 12 label 7+ label Sample Std Dev 1.43 1.39 1.69 2.01 Sample Mean 21 19 19 6.3 5.6 5.3 (a) What is the sum of all the data in the data set? T (b) What is the overall sample size for all groups combined?N- (c) What is the grand mean? (use three decimals in your answer) (d) Calculate the group sum of squares (aka treatment sum of squares), which is a measure of (you have one attempt) sample variation. SSG (use three decimal places in your answer) (e) Calculate the error sum of squares, which is a measure of (you have one attempt) sample variation SSE (use three decimal places in your answer) (f) Complete the ANOVA table. Note that you've already found two of the three sums of squares. Use three decimals for the sums of squares and means squares, then round the F test statistic to 2 decimals Source of Variation Treatment Error Total df Sum of Squares Mean Square (9) Do the data provide convincing evidence that the mean rating associated with the game description by 12- to 13-year-old boys is not the same for all four restrictive rating labels? Test the appropriate hypotheses using a significance level of 0.05 The appropriate hypotheses are: Ha: all of the population means are different Ha: at least one population mean is different 12: The test statistic is: The p-value is associated with this test statistic is 0.0040. Based on this, the statistical decision is to: (you have two attempts) At the 0.05 level, we (you have two attempts) that at least one mean rating differs significantly from the rest. Now we can test each mean against each other mean, and use a Bonferroni correction to control the family-wise error rate at α=0.05. Recall from above that: 18+-7.1 16+-6.3 12-5.6 T7-5.3 For each comparison, calculate the difference in sample means, the t-test statistic (rounded to three decimal places), and the p-value. The standard error and degrees of freedom for each comparison are provided Parameter difference in sample meansstandard error of difference ttest statistic degrees of freedomtwo sided p-value 0.51 0.52 0.52 0.52 0.52 0.53 40 38 38 38 38 36 According to these p-values, which differences in means are statistically significant using a comparison-wise error rate of 0.05 (i.e. no multiple comparisons correction)? You have just one attempt per group, and you may submit attempts one at a time. You should wait until you know you have the correct answers for the p-values above before answering these

Answer 1

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