Topic 1

An economist studies the family income in two countries of the European Union, country A and country B. He collects data pl=1,000 for households in country A and pr=1,500 households in country B. From the statistical analysis of the data on income, the following results.

Country A. Average estimated income 19,000 euros and variance 5,000 euros.

Country B: Average estimated income 20,200 euros and variance 6,400 euros,

(a) Consider whether the hypothesis that the average family income of country A is equal to 20,000 euros is statistically supported against the hypothesis that it is less than 20,000 euros. (UNITS 6)

(b) Consider whether the hypothesis that the average family income of country B is equal to 20,000 euros is statistically supported against the hypothesis that it is greater than 20,000 euros. (UNITS 6)

(c) Consider whether the hypothesis that the two countries have the same average family income is statistically supported (UNITS 6)

(d) To explore citizens' views on economic policy, households were asked whether they are optimistic about the future of the economy in their country. In country A out of 1,000 households 520 declared optimism, while in country B only 310 declared optimism. Find the 95% confidence interval for the difference in the percentages of households declaring optimism in the 2 countries. (UNITS 7)