1. [10 marks] Higher levels of HDL Cholesterol (sometimes called "good cholesterol") is associated with better cardiovascular health. Let x denote the HDL level of a randomly selected person. To test whether there is a difference between women and men, independent random samples of women and men were selected and their HDL levels were measured. The resulting summary statistics are given below. In X S Sample 1 (Women) 147 58.4 15.0 Sample 2 (Men) 153 49.1 14.5 Using these statistics, test the claim (at a 5% significance level) than on average women have higher HDL levels than men. For full marks, your answer must: . State the null and alternative hypotheses in appropriate symbols . Show your calculation of the test statistic and verify the requirements. (Do not use a "pooled variance" version of the test statistic.) . Show/explain how you calculated the P-value, including a sketch of the corresponding area. (Use the simple/conservative formula for of or you use technology to determine a more accurate P-value. Either is acceptable and it doesn't affect the conclusion in this case.) . State whether you reject or fail to reject the null hypothesis. . State you conclusion in terms of the original claim