Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 448 gram setting. It is believed that the machine is underfilling the bags. A 43 bag sample had a mean of 443 grams. Assume the population standard deviation is known to be 16. A level of significance of 0.02 will be used. State the null and alternative hypotheses.

Answer 1

Given :-

Sample Mean = 443

Population Standard Deviation = 16

Sample size n = 43

Population Mean

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-

Z = -2.049

Test Criteria :-

Reject null hypothesis if Z < -Z

Z= Z_0.02 = 2.05

Check the condition holds or not Z < -Z

-2.049 < - 2.05 does not satisfies the condition, hence we fail to reject null hypothesis

Conclusion :- Accept null hypothesis

Bag filling machine works correctly at the 448 gram setting.