Perform a t-test for Independent Groups. A researcher randomly selects a group o

Question

Perform a t-test for Independent Groups. A researcher randomly selects a group of participants and randomly assigns them to one of two conditions. The first group (condition) works on a complex problem in a room with no other person in the room. The second group performs the same complex task, but is observed by three strangers. The data below shows the number of errors for each group. Perform the appropriate analysis. Alone 4 5 3 6 Strangers 6 4 6 4 a.) What significance test did you use and what value did you obtain? b.) What is the critical value and what do you conclude?

Explanation / Answer

a.) What significance test did you use and what value did you obtain?

Let the level of significance be set at 0.05.

We use the independent two-sample t test. [answer, what test to use]

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    4.5          
X2 =    5          
              
Calculating the standard deviations of each group,              
              
s1 =    1.290994449          
s2 =    1.154700538          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    4          
n2 = sample size of group 2 =    4          
Thus, df = n1 + n2 - 2 =    6          
Also, sD =    0.866025404          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -0.577350269   [ANSWER, TEST STATISTIC]

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b)
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.446911851      
              
As |t| < 2.447,   WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Hence, there is no significant difference between the mean number of errors between the two groups at 0.05 level. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

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