a A doctor claims that the average Australian is more than 5 kg overweight. To test this claim, a random sample of 50 Australians were weighed, and the difference between their actual weight and their ideal weight was calculated. The mean and the standard deviation of that difference were 6.5 and 2.2 kg, respectively. Can we conclude at the 5% significance level that enough evidence exists to show that the doctor's claim is true. Step 1. Statement of the hypotheses (2 marks) Step 2. Test statistic and the standardised test statistic (0.5 mark) Step 3. Level of significance (0.5 mark) Step 4. Decision rule (2 marks) Step 5. Computation of the value of the test statistic (2 marks) Step 6. Conclusion (3 marks) (b) Consider the same question in part (a). Suppose that the population standard deviation is known to be 2.5 kg. Using this additional information repeat the test at the 5% level of significance that the average Australian is more than 5 kg overweight? Answer the following questions to arrive at your conclusion. 1. Test statistic and its sampling distribution (1 mark) Il Discuss whether there is change in the test statistic and/or its sampling distribution compared to part (a)(step 2) (1 mar k) ill Decision rule based on the standardised test statistic (1 mark) IV Value of the test statistic and Conclusion (1 mark)

step 1, Bratertiefit of the hypothesed (2 markn) Step 3. Eavet of tigrificance {0.5 matk Etep a. Becisich fule (2 markis) Stap 5, Corripetation of the value of the test stativite (2 markn) Step 6. Conciusion (3 marks ) questopht is artive at your conclineton. r Test slatistic and its sampling distribution ( 1 mark) 4. Discuss whether fhore is change in the tost statestio andior its samptiry distribution compared to part (a)(step 2) (1 mar k) ii Decision ruier based on the statidardised fest statistic (1. mark) IV Value of the test statistic and Canclusion ( 1 mark)