Question

In a Gallup poll conducted August 31–September 2, 2009, 513 national adults aged 18 years of age or older who consider themselves to be Republican were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?” The mean wasted was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 national adults aged 18 years of age or older who consider themselves to be Democrat. The mean wasted was found to be 41 cents with a standard deviation of 2.6 cents. Construct a 99% confidence interval for the mean difference in government waste, μ₁-μ₂, where μ₁ denotes the mean for republicans, and μ₂ denotes the mean for democrats.

a) The necessary conditions for constructing this confidence interval _____(are / are not) satisfied for this data.

b) The critical value needed for this confidence interval is t_α/2 =______ .

c) We are 99% confident that, on average, Republicans feel the government wastes between _______(lower) and _______ (upper) cents more out of every dollar than Democrats. Report your answers rounded to 3 decimal places, where applicable.

Answer 1