2A simple random sample of 50 adults is obtained and each pe

2.A simple random sample of 50 adults is obtained, and each person\'s red blood cell count (in microliter) is obtained. The sample mean is 5.23. The population standard deviation for red blood cell counts is 0.54. Use a .01 significance level to test the claim that the sample is from a population with a mean less than 5.4, which is a value often used for the upper limit of the range of normal values. (Be sure you show complete steps in hypothesis testing.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   5.4  
Ha:    u   <   5.4  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    -   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    5.23          
uo = hypothesized mean =    5.4          
n = sample size =    50          
s = standard deviation =    0.54          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.226076904          
              
Also, the p value is              
              
p =    0.013004515          
              
Comparing |z| < 2.326 (or, p > 0.01), we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is significant evidence that the sample is from a population with a mean less than 5.4. [CONCLUSION]