Question

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 435.0 gram setting. It is believed that the machine is underfilling the bags. A 40 bag sample had a mean of 430.0 grams. A level of significance of 0.01 will be used. Is there sufficient evidence to support the claim that the bags are underfilled? Assume the variance is known to be 576.00.

What is the conclusion?

There is not sufficient evidence to support the claim that the bags are underfilled.

OR

There is sufficient evidence to support the claim that the bags are underfilled.

Answer 1

null hypothesis:Ho Alternate Hypothesis:Ha 435 435 for 0.01 level with left tailed test, critical value of z- Decision rule: 2.326 reject Ho if test statistic z<-2.326 population mean sample mean sample size population std deviation 435 430.00 40.00 24.00 μέ standard errror of means σ -σ//ns 3.7947 test statistic z =(X-μ)/σ,- 1.318

from above as test statistic is not in critical region; we can not reject null hypothesis

There is not sufficient evidence to support the claim that the bags are underfilled.