Researchers wished to know if they could conclude that two populations if infant

Question

Researchers wished to know if they could conclude that two populations if infants differ with respect to mean age at which they walked alone. The following data (age in months) were collected:
Group A: 9.5 10.5 9.0 9.75 10.0 13.0 10.0 13.5 10.0 9.5 10.0 9.75
Group B: 12.5 9.5 13.5 13.75 12.0 13.75 12.5 9.5 12.0 13.5 12.0 12.0
What should the researchers conclude? Assume significance level alpha is 0.05.
(You need to set up the hypothesis, calculate the statistic, P-value and draw your conclusion)

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0   [HYPOTHESES]

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At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    10.375          
X2 =    12.20833333          
              
Calculating the standard deviations of each group,              
              
s1 =    1.396017062          
s2 =    1.449268363          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    12          
n2 = sample size of group 2 =    12          
Thus, df = n1 + n2 - 2 =    22          
Also, sD =    0.580893165          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -3.156059401   [TEST STATISTIC]      

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where uD = hypothesized difference =    0          
              
Also, using p values, as it is 2 tailed,              
              
p =    0.00458198   [P VALUE]

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As P < 0.05,    WE REJECT THE NULL HYPOTHESIS.      

Hence, there is significant evidence that two populations of infants differ with respect to mean age at which they walked alone 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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