Resturant Ass states that the mean household spends 3456 a y

Resturant Ass. states that the mean household spends $3456 a year on food you randomaly select 12 households a=.10 can you reject the resturants claim ? find the p value p= reject the ho or fail to reject and why?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   3456  
Ha:    u   =/   3456  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    11          
tcrit =    +/-   1.795884819      
              
Getting the test statistic, as              
              
X = sample mean =    3214.416667          
uo = hypothesized mean =    3456          
n = sample size =    12          
s = standard deviation =    898.2130197          
              
Thus, t = (X - uo) * sqrt(n) / s =    -0.931704614          
              
Also, the p value is              
              
p =    0.371487245          
              
Comparing |t| < 1.79588, (or p > 0.10), we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that the mean household spending is not $3456. [CONCLUSION]