Question

A cereal box filling machine is designed to release an amount of 12 ounces of cereal into each box, and the machine’s manufacturer wants to know of any departure from this setting. The engineers at the factory randomly sample 100 boxes of cereal and find a sample mean of 12.25 ounces. If we know from previous research that the population is normally distributed with a standard deviation of 1.51 ounces, is there evidence that the mean amount of cereal in each box is different from 12 ounces at 0.05 significance? State the hypotheses, check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 12
Alternative Hypothesis: μ ≠ 12

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (12.25 - 12)/(1.51/sqrt(100))
z = 1.66

P-value Approach
P-value = 0.0969
As P-value >= 0.05, fail to reject null hypothesis.

there is not significant evidence to conclude that the mean amount of cereal in each box is different from 12 ounces