Demographic Methods - Statistics Assignment Help

Assignment Task

Demographic Methods,

This assessment task requires you to (1) identify appropriate data and methods, calculate standardised death rates, and interpret the results; (2) explain and illustrate demographic concepts; and (3) calculate a life table and measures derived from that life table.

ASSESSMENT TASK

1. Consider a life table that measures the time in minutes from starting a marathon to completing a marathon. Everyone who starts, completes the marathon (no withdrawals). How would the life table elements q_x, l_x, L_x, T_x, e₀ and e_x be calculated or measured, and what would each of them represent? What would be the problem in measuring e₀ if some people did not complete the marathon, and how could this problem be resolved? (100 words)

2. Period life expectancy at birth for a particular country in 2020 was 80 years. Will babies born in that country in 2020 live—on average—for 80 years, less than 80 years, or more than 80 years? Justify and explain your answer with reference to a Lexis diagram you have created, showing relevant synthetic and real cohorts. (100 words)

3. Use the data in Table 1, and appropriate methods, to calculate a life table. Include at least the elements x, n, _nq_x, l_x, _nL_x, and e_x. All assumptions, element definitions, and equations used must be clearly stated. More detailed and accurate methods than the ‘rough estimate’ method for converting _n m_x to _n q_x will attract higher marks.

4. Assuming both male and female mortality in a country follows the mortality pattern in this life table (question 3) over a long period of time, answer the following. Show your reasoning and calculations, and list any assumptions made.

a. What is the probability that a newborn baby will die before her 80th birthday?

b. What proportion of 30–34-year-olds will survive for the next 5 years?

c. What is the probability that those now exact-age zero will survive to exact age 50 years but then die before exact age 60 years?

d. What proportion of newborn babies will die between their 50^th and 60^th birthdays?

e. A woman gives birth to twins on her 40^th birthday, and gives birth again to a singleton exactly 5 years later. What is the probability that the woman, and her 3 children, all survive to celebrate the woman’s 100^th birthday?

f. What is the probability that a woman aged in her 40s on 1 January 2030 will die before the beginning of 2040?

g. What is the average age at death for a man who reaches his 55^th birthday?

h. Assuming the country has no migration, estimate the number of female births that occurred over the 5 years 2010–14 given the male population aged 5–9 years at 1 January 2020 was 8,968.

i. If, instead, the country has a constant 10,000 births each year over a long period of time, and no migration, what is the total size of the country’s population?

j. The 2021 census showed there were 469 men aged 80+ years. Ignoring migration, what is the estimated size of the male population aged 70+ years at the 2011 census?

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