Confidence intervals

Problem

MORT = Total Mortality Rate per 100,000 Population

INCC = Per-Capita Income by State, in Dollars

POV = Proportion of Families Living Below the Poverty Line by State

ALCC = Per-Capita Consumption of Alcohol by State, in Gallons

TOBC = Per-Capita Consumption of Cigarettes by State, in Packs

PHYS = Physicians per 100,000 Population

AGED = Proportion of Population over the Age of 65

  1. Find a 95% confidence interval for \(β_{income}\)
  2. Find a 99% confidence interval for \(β_{tobacco}\)

Solution

  1. The critical value is \(t_{0.025,44}=2.015\) so \(0.00418±2.015⋅0.005367\) or \(-0.0066<β_{income}<0.015\)
  2. The critical value is \(t_{0.005,44}=2.692\) so \(1.69±2.692⋅0.301\) or \(0.88<β_{tobacco}<2.5\)