Dieticians claim that most adults do not intake enough dieta

Dieticians claim that most adults do not intake enough dietary fiber from food (not supplements). For optimal health, adults should intake an average of twenty-eight grams of fiber from food per day. Below is the amount of dilatory fiber from food consumed by twenty randomly selected adults. At the 5% significance level, can we conclude that the average amount of dietary fiber from food consumed per day is less than twenty-eight grams?

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   28  
Ha:    u   <   28  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    -   1.729132812      
              
Getting the test statistic, as              
              
X = sample mean =    19.25          
uo = hypothesized mean =    28          
n = sample size =    20          
s = standard deviation =    4.876096368          
              
Thus, t = (X - uo) * sqrt(n) / s =    -8.025105874          
              
Also, the p value is              
              
p =    7.99847E-08          
              
Comparing t < tcrit (or, p < 0.05), we   REJECT THE NULL HYPOTHESIS.      

There is significant evidence that the mean amount of dietary fiber from food consumed per day is less than 28 grams. [CONCLUSION]