Answer:
The calculated t- value = 1.09 > 3.19 at 0.025 level of significance
Null hypothesis is rejected
There is sufficient evidence to support the claim that the bags are underfilled
Step-by-step explanation:
<u><em>Step(i)</em></u>:-
Given the mean of the Population(μ)  = 419 grams
The sample size 'n' =19
Given mean of the sample x⁻ = 412
Given variance of the sample S² = 784
                                                  S = √784 = 28
<u><em>Step(ii)</em></u>:-
<u><em>Null hypothesis: H₀</em></u>: There is no sufficient evidence to support the claim that the bags are underfilled.
<u><em>Alternative hypothesis: H₁:</em></u>
 There is sufficient evidence to support the claim that the bags are underfilled.
Test statistic 
                      
                     
                    t = -1.09
                  |t| = |-1.09|
<em>Degrees of freedom   ν = n-1 = 19-1 =18</em>
<em>t₀.₀₂₅ =  3.19</em>
<u><em>Final answer:</em></u><em>-</em>
The calculated t- value = 1.09 > 3.19 at 0.025 level of significance
Null hypothesis is rejected
There is sufficient evidence to support the claim that the bags are underfilled