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Independent-Samples t-Test A researcher wants to assess if fasting cholesterol levels differ in Type A and...

Independent-Samples t-Test A researcher wants to assess if fasting cholesterol levels differ in Type A and Type B personality men (alpha= .05). Group 1 (Type A personality): 233, 291, 312, 250, 246, 197, 268, 224, 239, 239, 254, 276, 234, 181, 248, 252, 202, 218, 212, 325 Group 2 (Type B personality): 344, 185, 263, 246, 224, 212, 188, 250, 148, 169, 226, 175, 242, 252, 153, 183, 137, 202, 194, 213

Calculate the confidence intervals for the differences between means, compare to the SPSS results and interpret them.

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Answer #1

Sample #1   ---->   1
mean of sample 1,    x̅1=   245.05
standard deviation of sample 1,   s1 =    36.64
size of sample 1,    n1=   20
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   210.30
standard deviation of sample 2,   s2 =    48.34
size of sample 2,    n2=   20

Degree of freedom, DF=   n1+n2-2 =    38              
t-critical value =    t α/2 =    2.0244   (excel formula =t.inv(α/2,df)          
                      
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    42.8901              
                      
std error , SE =    Sp*√(1/n1+1/n2) =    13.5630              
margin of error, E = t*SE =    2.0244   *   13.5630   =   27.4569  
                      
difference of means =    x̅1-x̅2 =    245.0500   -   210.300   =   34.7500
confidence interval is                       
Interval Lower Limit=   (x̅1-x̅2) - E =    34.7500   -   27.4569   =   7.2931
Interval Upper Limit=   (x̅1-x̅2) + E =    34.7500   +   27.4569   = 62.2069

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