MATHS- The HSE are interested in the effectiveness of a new flu vaccine

1. The HSE are interested in the effectiveness of a new flu vaccine before rolling it out to the public. They therefore conducted a survey to evaluate the effectiveness of the new vaccine. The vaccine was provided in a 2-shot sequence over 2 weeks. Some study participants received the 2-shot sequence, some only appeared for the first shot and others received no vaccine. The following spring, the study participants were surveyed to determine whether or not they had suffered from flu since the study started. The following results were obtained:No vaccine 1-shot 2-shotFlu 24 9 13N0 – Flu 289 100 565The HSE employ you as a statistician to help them analyze the results of their study.(a) Do the data present evidence to indicate that the incidence of flu is dependent on theamount of flu treatment?[20](b) Write a short paragraph (max. 100 words), in layman’s language, presenting your con- clusions from analyzing the data to the HSE and detailing the practical recommendationyou would make about rolling out the flu vaccine.[20] [Total: 40 marks]2. An assembly line manager in a factory believes that some assembly lines in the factory are not as productive as others. He looks at the number of units produced on each of 8 assembly lines in the past 10 daysAssembly line 1 2 3 4 5 6 7 8Units produced 45 52 48 38 60 55 43 59Are the manager’s suspicions reinforced by the data? (Take a 1% significance level.)[Total: 20 marks]3. A psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data were recorded. Determine the equation of the regression line and graph the line on a scatter plot.Hours without Sleep ? Number of Mistakes???32 638 848 1324 546 735 630 534 842 12