Hypothesis testing for mean with known population standard deviation.
A fast food restaurant strives to serve 80 customers per hour during its peak lunch hour. It samples 30 shifts (i.e. 30 peak lunch hours) to resolve whether it is meeting this expectation. The sample mean is 75 customers. The population standard deviation is known to be 10.
i. Set up a null and alternative hypothesis to test whether this sample is falling below expectations.
ii. Conduct this hypothesis test at the 5% level of significance.
Comment on whether you believe this is better to be conducted as a 1-sided or 2-sided test.