Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 440 gram setting. It is believed that the machine is underfilling the bags. A 21 bag sample had a mean of 430 grams with a standard deviation of 29 . Assume the population is normally distributed. A level of significance of 0.02 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places

Answer 1

Null hypothesis  

              
                  
Alternative hypothesis

               
                  
We have for given sample,                  
Population mean for given sample=440  
Sample mean=430          
Sample standard deviation s=29      
Sample size =n=   21          
                  
Degree of freedom = n-1 =20      
                  
  
                  
t test statistic formula is

P value is 0.0649......................by using Excel command TDIST(-1.58,20,1)

0.05< P value < 0.10

P value is 0.0649>0.02

Therefore, we fail to reject H0 at  level of significance of 0.02 .

Conclusion: We do not have sufficient evidence at  level of significance of 0.02 to say that ,the machine is underfilling the bags.