Biostatistics for epidemiology

INSTRUCTIONS: ANSWER ALL QUESTIONS Q1 a) Describe the properties of a normal distribution (5 marks) b) Distinguish between skewness and kurtosis (5 marks) c) Describe the three main types of kurtosis (6 marks) d) Consider the distribution of weight gains W of a population of calves with a mean weight of 200 kg and a standard deviation of 35 kg. What is the probability of a calf in this population to have a weight equal or less than 185kg? (3 marks) e) Given a normally distributed population with a mean of 120 and a standard deviation of 30, find: i) Pr (x ≥70) (3 marks) ii) Pr (60 ≤ x ≤180) (3 marks) Q2 People with blood sodium levels of greater than 145 mEq/l are considered at risk of circulatory illnesses. An advice programme was set up to teach people how to control their sodium levels by altering their diet. Twenty-seven (27) people were entered into this programme. The difference in blood sodium levels before and after participating in the programme are shown in Table 1. Table 1 a) b) c) Participant Blood sodium level before programme Blood sodium level after programme Difference in blood sodium level 1 149 153 -4 2 157 139 18 3 145 158 -13 4 154 156 -2 5 152 138 14 6 146 149 -3 7 150 158 -8 8 149 139 10 9 147 154 -7 10 154 149 5 11 156 157 -1 12 147 148 -1 13 156 137 19 14 157 141 16 15 155 143 12 16 157 149 8 17 151 141 10 18 145 151 -6 19 147 138 9 20 150 142 8 21 155 136 19 22 147 143 4 23 146 145 1 24 149 135 14 25 152 146 6 26 153 144 9 27 156 142 14 151.1852 4.104754 145.5926 7.088774 5.592593 9.001108 mean Sd Are these data quantitative or qualitative in nature? (3 marks) Are these data paired or unpaired in nature (justify your answer)? (3 marks) What is the mean difference in blood sodium levels before and after the advice programme? (3 marks) d) i) e) d) Calculate the 95% confidence interval of this difference ii) the 99% confidence interval of this difference. marks) (5 marks) (5 Carry out a hypothesis test to see if this difference is significant and interpret the resultant P value.