- 1 16 Marks The Body Mass Index Bmi Is Calculated By Dividing A Person S Weight By The Square Of His Or Her Height 1 (87.44 KiB) Viewed 26 times
1. (16 marks) The body mass index (BMI) is calculated by dividing a person's weight by the square of his or her height; it is a measure of the extent to which the individual is overweight. For the general population of middle-aged men, the mean of the distribution of BMI is 26.0 kg/m² and the standard deviation is 2.5 kg/m². For the population who later develop diabetes, the distribution of BMI has an unknown mean y and a standard deviation o. A sample of 16 men selected from this group has mean 27.0 kg/m2 and a standard deviation 2.8 kg/m². (a) Construct a 95% confidence interval for the population mean j. (4 marks) (b) At the 0.05 significance level, test whether the mean BMI for the population of middle-aged men who do develop diabetes is greater than the general population of middle-aged men. (8 marks) (c) Assume there is no differences between the means of two populations. If the test is repeated for three independent samples, is it more (or less) likely that at least one of them will reject the null hypothesis in (b) than it is for a single test? (4 marks)