In the general population of healthy young adults bone miner

In the general population of healthy young adults, bone mineral density is Normally distributed, and density scores are standardived to have a mean of 0 and standard deviation of 1. A study examined the bone densities of a random sample of 28 adult men suffering from chronic hepatitis c infections. their mean standardized bone density was -0.61. Does this provide good evidence that the mean standardized bone density of adult men suffering from chronic hepatitis C infection is less than 0?

Solution

We assume alpha = 0.05 as it is not given here.

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Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   0  
Ha:    u   <   0  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    27          
tcrit =    -   1.703288446      
              
Getting the test statistic, as              
              
X = sample mean =    -0.61          
uo = hypothesized mean =    0          
n = sample size =    28          
s = standard deviation =    1          
              
Thus, t = (X - uo) * sqrt(n) / s =    -3.227816599          
              
Also, the p value is              
              
p =    0.001631828          
              
As |t| > 1.703, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is sufficient evidence that the mean standardized bone density of adult men suffering from chronic hepatitis C infection is less than 0. [CONCLUSION]