A study in Pittsburgh measured various cardiovascular risk factors in children a

Question

A study in Pittsburgh measured various cardiovascular risk factors in children at birth and during their first 5 years of life. In particular, heart rate was assessed at birth, 5 months, 15 months, 24 months, and annually thereafter until 5 years of age. Heart rate was related to age, sex, race, and socioeconomic status. The data in Table 3 were presented relating heart rate to race among newborns

Table 3. Mean heart rate for white and black groups.

Determine whether there is a significant difference in mean heart rate between Caucasian and African- American newborns (=0.05). Report a p-value for two-sided alternative).

Explanation / Answer

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 =    125          
X2 =    133          
              
Calculating the standard deviations of each group,              
              
s1 =    11          
s2 =    12          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    218          
n2 = sample size of group 2 =    156          
Thus, df = n1 + n2 - 2 =    372          
Also, sD =    1.215780735          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -6.580133878          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   1.966361504      
              
              
Also, using p values,              
              
p =    1.59913*106-10   [ANSWER, P VALUE]      
              
As |t| > 1.966, and P < 0.05,    WE REJECT THE NULL HYPOTHESIS.          

Hence, there is a significant difference in mean heart rate between Caucasian and African- American newborns at 0.05 level. [CONCLUSION]

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