Answer:
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 447 gram setting.
[tex]H_0:\mu = 447\\H_a:\mu\neq 447[/tex]
Mean = [tex]\mu = 447\\s = 21\\x = 443[/tex]
n = 19
Since n < 30 , so we will use t test
[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]
Substitute the values :
[tex]t=\frac{443-447}{\frac{21}{\sqrt{19}}}[/tex]
[tex]t=−0.8302[/tex]
t calculated = -0.830
degree of freedom = n-1 = 19-1 = 18
A level of significance=α=0.025
[tex]t_{(df,\frac{\alpha}{2})}=2.093[/tex]
t critical = 2.093
t calculated < t critical
So, We failed to reject null hypothesis
Decision rule -0.830< 2.093 So, We failed to reject null hypothesis
