(a)[5]
At the $2.5\%$ significance level, test whether the mean mass of cereal boxes filled by the machine has decreased.
(b)[5]
If the actual mean mass is $506$ grams, find the probability of a Type II error.
Mathematics 9709 · AS & A Level · Hypothesis testing
Hypothesis testing — practice question
The masses of cereal boxes packed by one particular machine have mean $510$ grams. The machine is then adjusted, and an inspector wants to check whether the mean mass of cereal boxes filled by the machine has fallen.
Once the adjustment has been made, he takes a random sample of $120$ cereal boxes. The sample mean mass is $508$ grams.
Assume that the standard deviation of the masses is $10$ grams.