Fat contents in percentage for 10 randomly selected hot dogs

Fat contents (in percentage) for 10 randomly selected hot dogs were given in the article \"Sensory and Mechanical Assessment of the Quality of Frankfurters\". Use the following data to construct a 90% confidence interval for the true mean fat percentage of hot dogs:
Note: you should carry at least 5 decimal precision for any intermediate calculations then round your answer as indicated in the problem

A)  x =  
    Note: round this answer to 1 decimal place precision

B) s =  
    Note: round this answer to 1 decimal place precision

C) t* =  
    Note: round this answer to 2 decimal place precision

D) Low:  % to High:  %

Solution

A)

Using technology,

X = sample mean =    22.51   [ANSWER]

b)

Using technology,

s = sample standard deviation =    4.515762517 [ANSWER]

c)

As df = 10 - 1 = 9, then for 90% confidence,
      
t(alpha/2) = critical t for the confidence interval = 1.833112933   [ANSWER]

********************      

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    22.51          
t(alpha/2) = critical t for the confidence interval =    1.833112933          
s = sample standard deviation =    4.515762517          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    19.89229733          
Upper bound =    25.12770267          
              
Thus, the confidence interval is              
              
(   19.89229733   ,   25.12770267   ) [ANSWER]