According to an IT magazine, the average payback period for IT purchases for medium-sized companies is 2.8 years. A random sample of fifty medium-sized companies led to the following following results: Average payback period: 3.1 years Standard deviation: 1.2 years. The following counter-assumption is made: the average payback period for IT purchases is The following counter-assumption is made: the average payback period for IT purchases is higher than that specified by the IT magazine. computer magazine. a) Specify in statistical form the hypotheses to be tested. b) Specify the decision rule, for a significance level of 1%. c) Perform the statistical test and indicate which hypothesis is favoured at the 1% level of significance level. Explain.