The government reported that mean daily coffee consumption f

The government reported that mean daily coffee consumption for adults is 1.65 cups. A sample of 38 adults from Las Vegas consumed mean of 1.84 cups with standard deviation of .85 cups. At 0.05 level of significance, could adults from Las Vegas be considered significantly different from US adults?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   1.65  
Ha:    u   =/   1.65  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha/2 =    0.025          
zcrit =    +/-   1.959963985      
              
Getting the test statistic, as              
              
X = sample mean =    1.84          
uo = hypothesized mean =    1.65          
n = sample size =    38          
s = standard deviation =    0.85          
              
Thus, z = (X - uo) * sqrt(n) / s =    1.377927836          
              
Also, the p value is              
              
p =    0.16822557          
              
Comparing z > 1.95996 (or, p > 0.05 ), we   FAIL TO REJECT THE NULL HYPOTHESIS.      

Thus, there is no signficant evidence that daults from Las Vegas are significantly different from US adults. [conclusion]