Supplementary exercise 6.46 of IPS7e ------------------------------------ Stating null and alternative hypotheses for mu (population mean). (a) The description indicates that the researcher (tenant group) is only interested in whether the apartments are smaller than advertised. Therefore it is valid to use a one-sided alternative hypothesis. H0: mu=1250 Ha: mu<1250 Note that the hypothesis representing the desired conclusion is given as the alternative hypothesis, not the null hypothesis. This is because the strongest test conclusion is a rejection of H0 and hence an adoption of Ha. (b) Again the description invites a one-sided alternative hypothesis, H0: mu=32 Ha: mu>32 The description does not specify what data should be used to assess the claims. If a single value for mileage is computed after 3000 miles, it is not clear how this can be used for inference, because we would not know what its standard deviation (or standard error, if we're thinking about this value as our estimate) would be. If instead mileage was computed after each trip to the gas station to fill up gas, there would be a long series of values on which inference could be based. (c) Here the description explicitly mentions that there is interest in both directions of deviations (larger or smaller) from the optimal value. H0: mu=5 Ha: mu<>5