Question

A study was conducted among children aged 8-10 to determine if resting heart rate differed between males and females. Independent samples of 8 females and 8 males were selected from the two respective populations.

The results were as follows (heart rates in beats/min):

Females 71, 80, 80, 75, 78, 77, 81, 82

Males 71, 81, 79, 74, 73, 78, 71, 74

Assume the samples were drawn from normally distributed populations with equal variance.

a) Use α = 0.05 (two-tailed) and assume 80% power.

b) State the null and alternative hypotheses.

c) List the critical value

d) Perform the appropriate statistical test using the attached SAS file.

e) If the decision was to fail to reject Ho, can Ho be accepted?

Answer 1

Hypothesis:

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 ╪   0         

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Degree of freedom, DF=   n1+n2-2 =    14                  
t-critical value , t* = ± 2.145   (excel formula =t.inv(α/2,df)      

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Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   1                  
mean of sample 1,    x̅1=   78.000                  
standard deviation of sample 1,   s1 =    3.625                  
size of sample 1,    n1=   8                  
                          
Sample #2   ---->   2                  
mean of sample 2,    x̅2=   75.125                  
standard deviation of sample 2,   s2 =    3.758                  
size of sample 2,    n2=   8                  
                          
difference in sample means =    x̅1-x̅2 =    78.0000   -   75.1   =   2.88  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    3.6924                  
std error , SE =    Sp*√(1/n1+1/n2) =    1.8462                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   2.8750   -   0   ) /    1.85   =   1.5572
                          
       
Decision:   | t-stat | < | critical value |, so, Do not Reject Ho                     
  
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There is not enough evidence of significant mean difference