A polling company is interested for the monthly household income in urban and rural areas. For this purpose, the company randomly selects 10 houesholds from urban areas and 10 households from rural areas. The table below shows the monthly income (in euro) of the selected households.

(a) Provide a point estimate for the mean income of the households. Provide also a point estimate for the variance of the income. Calculate 95% confidence intervals for the mean and the variance.

(b) Provide a point estimate for the mean income of the households in rural areas. Provide also a point estimate for the variance of the income in rural areas. Calculate 90% confidence intervals for the mean and the variance of the income in rural areas.

(c) Examine statistically the hypothesis that the mean income in rural areas is the same with the mean income in urban areas.

(d) The government stated recently that the percentage of households living below the poverty line is less than 10%. Examine if this statement is supported by statistical evidence. (Note: Poverty line

I Urban Area Rural Area 4 5 6 7 8 3200 900 1050 1100 2300 1300 5500 1 2 3 3500 2600 500 1600 2200 960 1000 9 5800 2100 1300 1500 10 1200 1300