Question

1. 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.

A professor at UCI wants to see what students really remember from their elementary school days, the stuff that was taught or the stuff that was popular at the time. She put together two tests, one with elementary school education questions and one about pop culture from that time. She got a sample of 9 students and had them take both tests. What test does she use?

Pop Culture:    65           52           90           72           59           79           80           68           76

Education:        65           74           87           96           84           80           82           89           75

Answer 1

  C: t-test for the difference between means for two related samples

	sample 1	sample 2	Di	(Di - Dbar)²
sum =	565	657.00	-92.000	1082.000

Ho :   µd=   0                  
Ha :   µd ╪   0                  
                          
Level of Significance ,    α =    0.05                  
                          
sample size ,    n =    8                  
                          
mean of sample 1,    x̅1=   70.625                  
                          
mean of sample 2,    x̅2=   82.125                  
                          
mean of difference ,    D̅ =ΣDi / n =   -11.5000                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    12.4327                  
                          
std error , SE = Sd / √n =    12.4327   / √   8   =   4.3956      
                          
t-statistic = (D̅ - µd)/SE = (   -11.5   -   0   ) /    4.3956   =   -2.616
                          
Degree of freedom, DF=   n - 1 =    7                        
                          
p-value =        0.0346   [excel function: =t.dist.2t(t-stat,df) ]               
Decision:   p-value <α , Reject null hypothesis     

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