Project #28043 - Short Stats HW

 
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All multiple choice questions have two submissions.

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. 

Group Sample Size Sample Mean Sample Std Dev
7+ label 10 6 2.04
12+ label 10 7.1 1.58
16+ label 10 7.9 1.55
18+ label 10 8 1.65


(a) What is the sum of all observations in the data set? T =  

(b) What is the grand mean? (x^^\_)^^\_ =  
(use three decimals in your answer) 

(c) Calculate the treatment sum of squares, which is a measure of  sample variation. 

SSTr =  
(use four decimals in your answer) 

(d) Calculate the error sum of squares, which is a measure of  sample variation. 

SSE =  
(use four decimals in your answer) 

(e) Complete the ANOVA table. Note that you've already found two of the three sums of squares. Use four decimals for the sums of squares and means squares, then round the F test statistic to 2 decimals. 

Source of Variation df Sum of Squares Mean Square F
Treatment
Error X
Total X X


(f) 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 0.01.

The appropriate hypotheses are:
    
The significance level is:  

The test statistic is:  

The p-value is:  

The statistical decision is to:  

At the 0.01 level, we  conclude that at least one of true mean ratings is different.
 

 
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Refer to the one-way ANOVA example about box compression strengths that we went over in class (pg 144 in your notes). Recall that the sample mean compression strengths for the four box types were

(x_1)^^\_ = 713.00 (x_2)^^\_ = 741.27 (x_3)^^\_ = 698.07 (x_4)^^\_ = 562.02

The results of the one-way ANOVA F test were that at least one of the box types had a different mean compression strength. From the boxplots, we were pretty sure that box type 4 was the one that was different. To verify this, let's look at the Tukey-Kramer 95% confidence intervals.

a) How many TK confidence intervals should be constructed?  

b) Compute the appropriate point estimates for the TK confidence intervals below. Decide whether 0 is in each CI and whether we can conclude that the population means are significantly different or not. Note that you only have one submission for the drop-box questions.

Box Types Difference Confidence Interval 0 in the CI? Means same or different?
1 & 2 mu_1-mu_2  ± 67.76
1 & 3 mu_1-mu_3  ± 67.76
1 & 4 mu_1-mu_4  ± 67.76
2 & 3 mu_2-mu_3  ± 67.76
2 & 4 mu_2-mu_4  ± 67.76
3 & 4 mu_3-mu_4  ± 67.76

Subject Mathematics
Due By (Pacific Time) 04/17/2014 11:30 pm
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