Using the Hypothesis testing and statistic Z- test we , find that the bag sample is not underfilled at a significance level of 0.025 i.e., 25% .
In the given question, we shall check the bag is underfilled at given level or not .
We can use the hypothesis testing, The Null and Alternative hypothesis are given as below :
H₀ : u = 411 : the bags are not underfilled
Hₜ : u < 411 : the bags are underfilled
Check it now using statistic Z-test and the test Statistic formula is given by
= ( M – u ) / S.D / √n , where M = mean of sample and S.D = standard deviations n is the number of bags used .
From given data we get, n= 19 ; M = 437 ; S.D = √ variance = √ 441 = 21
Including all of the above variables in formula
Z = (437-411)/21/√19
= 26/21/√19
= 5.395
This is right -tail test in statistic Z -test
P- value = 1 – 0.9999 = 0.111 ( by using Z-table or P-value for Z in Excel )
The sufficient evidence level is 0.025 i.e., alpha (α) = 0.025
P- value >α , this implies that Null hypothesis is not Rejected .
There is sufficient evidence to suggest that bag is not underfilled.
To learn more about Hypothesis testing, refer:
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