Question

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

Answer 1

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.

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.