The management asks you to say with 99% certainty that the change from yellow to blue packaging will lead to better sales. The yellow packaging led to weekly sales of 10,000 packages on average. The sample of 100 stores from the 5500 Tasty Markets showed weekly sales of 10,050 packages for the blue packaging with an empirical standard deviation of S_emp = 360 packages.

(a) Use the example to formulate the test hypotheses so that the α-error is the worst error.

(b) Identify the corresponding β-error.

(c) Test whether the demand of company management is fulfilled under these circumstances.

(a) How large must the sample size be—ceteris paribus—so that the lower limit of a one-sided confidence interface (α = 5%) is at least 9950 packages?