Question

For the following experiment/question, pick the most appropriate statistical test. You have the following statistical tests as choices: some may be used more than once, others not at all.  Assume homogeneity of variance (where applicable) and the validity of parametric tests (where applicable), unless something is directly stated (e.g., “the data are not at all normal”) or otherwise indicated (viz., by the inspection of the data) which would indicate a strong and obvious violation of an assumption. This means you must inspect the data for violations of all assumptions. Unless it is stated that the population parameter is known, assume it isn’t. Please do not concern yourself with any intervening variable that you may perceive. Finally, please don’t think about what the data would look like in reality. Assume that the question represents reality.  Please simply write the letter for the test as your answer. [You can, but need not, add an explanation.] If none of the tests are appropriate, the answer is P) none of the above. Here are the tests:  A: one sample z-test    B: one-sample t-test   C: t-test for the difference between means for two related samples  D: t-test for the difference between means for two independent samples with homogeneity of variance  E: t-test for the difference between means for two independent samples with heterogeneity of variance   F: a one sample z-test for proportions (or a chi-square goodness of fit)   G:  chi-square goodness of fit only (where a one sample z-test of proportions isn’t appropriate) H: a two-sample z-test for the difference between proportions (or a chi-square test of independence) I:  chi-square test of independence only (where a two-sample z-test for the difference between proportions isn’t appropriate.)  J:  simple regression             K: multiple regression L:  one-way ANOVA M: two-way ANOVA N: Mann-Whitney O:  Wilcoxon P: none of the above.

Does watching Barney increase altruism in children? Amanda put nine kids in a room where they watched Barney and another nine kids is a quiet room without television. Then the kids filled out a questionnaire that determined their altruism score (which we can assume to be interval). The scores are:

                Barney: 43, 55, 63, 57, 77, 65, 84, 73, 66

                Quiet:     67, 55, 74, 63, 56, 33, 45, 53, 47

Answer 1

D: t-test for the difference between means for two independent samples with homogeneity of variance

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 >   0                  
                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   64.778                  
standard deviation of sample 1,   s1 =    12.357                  
size of sample 1,    n1=   9                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   54.778                  
standard deviation of sample 2,   s2 =    12.357                  
size of sample 2,    n2=   9                  
                          
difference in sample means =    x̅1-x̅2 =    64.7778   -   54.8   =   10.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    12.3570                  
std error , SE =    Sp*√(1/n1+1/n2) =    5.8251                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   10.0000   -   0   ) /    5.83   =   1.72
                          
Degree of freedom, DF=   n1+n2-2 =    16                  
t-critical value , t* =        1.746   (excel function: =t.inv(α,df)              
Decision:   | t-stat | < | critical value |, so, Do not Reject Ho                      

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