A simple random sample of 55 adults is obtained from a norma

A simple random sample of 55 adults is obtained from a normally distributed population, and each person\'s red blood cell count (in cells per microliter) is measured. The sample mean is 5.19 and the sample standard deviation is 0.53 . Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4 comma which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?

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 =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    5.19          
uo = hypothesized mean =    5.4          
n = sample size =    55          
s = standard deviation =    0.53          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2.93849374          
              
Also, the p value is              
              
p =    0.001649057          
              
Comparing |z| > 1.645 (or, p < 0.05), we   REJECT THE NULL HYPOTHESIS.          
              
Thus, there is significant evidence that the sample came from a population with mean less than 5.4. [CONCLUSION]