One water quality standard for water that is discharged into

One water quality standard for water that is discharged into a particular type of stream or pond is that the average daily water temperature be at most 18°C. Six samples taken throughout the day gave the data:

16.8, 21.5,19.1,12.8,18.0,20.7

The sample mean x=18.15 exceeds 18, but perhaps this is only sampling error. Determine whether the data provide sufficient evidence, at the 10% level of significance, to conclude that the mean temperature for the entire day exceeds 18°C.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   18  
Ha:    u   >   18  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    5          
tcrit =    +   1.475884049      
              
Getting the test statistic, as              
              
X = sample mean =    18.15          
uo = hypothesized mean =    18          
n = sample size =    6          
s = standard deviation =    3.133528363          
              
Thus, t = (X - uo) * sqrt(n) / s =    0.117255508          
              
Also, the p value is              
              
p =    0.455611017          
              
Comparing t < 1.476 (or, p > 0.05), we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the mean temperature for the entire day exceeds 18°C. [CONCLUSION]