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A machine that is programmed to package 1.20 pounds of cereal in each cereal box is being tested for its accuracy. In a sample of 36 cereal boxes, the mean and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.Select the null and the alternative hypotheses to determine if the machine is working improperly, that is, it is either underfilling or overfilling the cereal boxes. Use the .05 level of significance.

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akiran007

Answer:

As the calculated value of z= 2 lies in the critical region  z ≥ z∝/2= ± 1.96 the null hypothesis is rejected that the machine is working improperly and it is either underfilling or overfilling the cereal boxes

Step-by-step explanation:

Here n= 36

Sample mean  = x`= 1.22

Required Standard mean  = u= 1.20

Sample Standard deviation = s=  0.06

Level of Significance.= ∝ = 0.05

The hypothesis are formulated as

H0: u1=u2   the machine is working properly

against the claim

Ha: u1≠u2

i.e the the machine is not filling properly

For two tailed test  the critical value is  z ≥ z∝/2= ± 1.96

The test statistic

Z= x`-u/s/√n

z= 1.22-1.20/0.06/√36

z= 2

As the calculated value of z= 2 lies in the critical region  z ≥ z∝/2= ± 1.96 the null hypothesis is rejected that the machine is working improperly and it is either underfilling or overfilling the cereal boxes

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