12 6 points A sample of 12 digital temperature of a certain

12. [6 points] A sample of 12 digital temperature of a certain type was selected, and each was tested in an oven where the true temperature was 100 C. The resulting readings were as follows: 104.3 89.6 89.9 95.6 9.2 90.0 98.8 103.7 98.3 106.4 102.0 91.1 With: s = 6.1095 Do these data suggest that the thermometers\' perform under these conditions diff from 100 C? State and test the appropriate hypotheses using alpha = .05.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   100  
Ha:    u   =/   100  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +/-   2.20098516      
              
Getting the test statistic, as              
              
X = sample mean =    97.075          
uo = hypothesized mean =    100          
n = sample size =    12          
s = standard deviation =    6.109474758          
              
Thus, t = (X - uo) * sqrt(n) / s =    -1.658489089          
              
Also, the p value is              
              
p =    0.125430773          
              
As |t| < 2.201, or P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the thermometer\'s mean reading under these conditions is different from 100 degrees C. [CONCLUSION]