Stating the hypotheses. In each of the following situations a significance test for a population mean µ is called for. Identify the null hypothesis H0 and the alternative hypothesis HA in each case. Make sure to use proper notation! (e.g. H0 : µ = µ0). For each question, all possible options involve µ and ¯x are available.

(a) Last year the mean sales per week in a large department store was $85,492. A manager wants to test the hypothesis that sales have increased since he was promoted.

(b) The mean length of steel beams manufactured by a properly-working machine is 3.2 meters. An industrial engineer wants to make sure that the machine in not operating incorrectly.

(c) A consumer advocate claims that the mean price for a cellular phone is not $300.

(d) The population mean IQ is 100. A psychologist wants to test the hypothesis that a new cognitive treatment increases the IQ of patients who undergo the treatment.