A study was conducted to compare the resting pulse rate among smokers and non-sm

Question

A study was conducted to compare the resting pulse rate among smokers and non-smokers. The data are summarized in the table below. The pulse rate distribution in each group can be assumed to be normal, and equal population variances can be assumed in the two groups

Conduct the appropriate test to see if the mean resting pulse rate for smokers is higher than that for non-smokers. Show all work and include all steps (hypotheses, rejection region, p-value, decision and conclusion) for full credit.

Explanation / Answer

Let

u1 = mean resting pulse rate for smokers
u2 = mean resting pulse rate for nonsmokers

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    right   tailed test.      
Calculating the means of each group,              
              
X1 =    76.4          
X2 =    73.7          
              
Calculating the standard deviations of each group,              
              
s1 =    4          
s2 =    3.2          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    35   , n2 =    40  
              
Then              
              
S =    3.594821237          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    0.832039439          
              
As ud = the hypothesized difference between means =    0   , then      
              
z = [X1 - X2 - ud]/Sd =    3.245038484          
              
Getting the critical value using table/technology, as this is right tailed 0.05 level,

zcrit = 1.645

Hence, we reject Ho when z > 1.645. [ANSWER, REJECTION REGION]

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Getting the p value using table/ technology,              
              
p = 0.000587174 [ANSWER, P VALUE]

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As z < 1.645, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.   [DECISION]      

Hence, there is significant evidence at 0.05 level that the mean resting pulse rate for smokers is higher than that for non-smokers. [CONCLUSION]

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