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manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 433.0 gram setting. It is believed that the machine is underfilling the bags. A 40 bag sample had a mean of 431.0 grams. A level of significance of 0.1 will be used. Is there sufficient evidence to support the claim that the bags are underfilled

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akiran007

Answer:

Since the calculated value of Z= -0.01871 does not lie in the critical region

Z ≄ Z∝ =± 1.28 we conclude that the null hypothesis is true and there is not sufficient evidence to support the claim that the bags are under filled.

Step-by-step explanation:

We formulate hypotheses as

H0: u < 433.0   against  the claim  Ha: u ≄ 433.0  ( one sided)

The significance level ∝= 0.1

Since the sample size n= 40 is greater then 30 z test is used.

Z = X`- u/ S/ √n

Z= 431.0- 433/ 676/√40

z= -2/106.8859

Z= -0.01871

The critical region is Z ≄ Z∝ =± 1.28 for one tailed test at alpha= 0.1

Since the calculated value of Z does not lie in the critical region we conclude that the null hypothesis is true and there is not sufficient evidence to support that the bags are under filled.

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