It is assumed that the mean systolic blood pressure is mu 1

It is assumed that the mean systolic blood pressure is mu = 120 mm Hg in the general population. In the Honolulu Heart Study, a sample of n = 25 people had an average systolic blood pressure of 130 mm Mg with a standard deviation of 20mm Hg. Is the group significantly different from the regular population? What are the null and alternative hypothesis? Ho: mu = 130 HA: mu > 130 Ho: mu = 130 HA: mu 130 Ho: mu = 120 HA: mu > 120 Ho: mu = 120 HA: mu 120 What is the test statistic? 2.5 -2.5 0.5 -0.5 What is the result of your test? alpha = 0.01

Solution

a)

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

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b)

At level of significance =    0.05          

As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    50          
X2 =    35          
              
Calculating the standard deviations of each group,              
              
s1 =    18          
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 =    12          
n2 = sample size of group 2 =    15          
Thus, df = n1 + n2 - 2 =    25          
Also, sD =    6.049793385          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.479423518 = 2.5 [ANSWER, I]

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c)      
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    +/-   2.05953855

As t > 2.0595, WE REJECT THE NULL HYPOTHESIS.      

Hence,

OPTION I: There is enough evidence that the group is significantly different from the regular population.

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