Let x be a random variable that represents red blood cell co

Let x be a random variable that represents red blood cell counts (RBC) with a normal distribution. For the population of healthy female adults, the mean is about 4.6. Suppose that a female patient has taken six laboratory blood tests and the RBC count data are as follows: {4.9, 4.2, 4.5, 4.1, 4.4, 4.3}. Given the sample, x = 4.40 and s = 0.28. Does the given data indicate that the RBC mean for this patient is lower than 4.6? Use alpha =.01.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   4.6  
Ha:    u   <   4.6  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    5          
tcrit =    -   3.364929999      
              
Getting the test statistic, as              
              
X = sample mean =    4.4          
uo = hypothesized mean =    4.6          
n = sample size =    6          
s = standard deviation =    0.28          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.749635531          
              
Also, the p value is              
              
p =    0.070294186          
              
As |t| < 3.365, and P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the mean RBC level for this patient is less than 4.6. [conclusion]