Question

8. (10 pts) An economist wants to determine if there is a linear relationship between the more educated a county is and income growth in that county. She takes a random sample of 7 counties in the state and records the percentage of the county population with at least a bachelor’s degree from college and the percentage growth in county per capita income over the past five years. Test her hypothesis at the 0.05 level of significance.

% of population with bachelor′s degree: 6.7, 12.6, 8.5, 14.7, 8.1, 11.4, 9.9

% growth in per capita income: 11.0,   29.4, 16.5, 37.1, 23.4, 33.0, 17.0

Answer 1

using minitab>stat>basic stat>correlation

we have

Correlation: % of poulation, % growth

Pearson correlation of % of poulation and % growth(r) = 0.892
P-Value = 0.007

t at 0.05 with 5 df is 2.5705

since t > 2.5705 so we reject Ho and conclude that there is a linear relationship between the more educated a county is and income growth in that county