We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background .
We define a \Delta \chi ^ { 2 } statistic , simulate the measurements of MAXIMA-1 and COBE , determine the probability distribution of the statistic , and use it and the data to set confidence intervals on several cosmological parameters .
We compare the frequentist confidence intervals to Bayesian credible regions .
The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15 % , and confidence interval-widths that agree within 30 % .
The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis .
The frequentist analysis gives values of \Omega = 0.89 { +0.26 \atop - 0.19 } , \Omega _ { B } h ^ { 2 } = 0.026 { +0.020 \atop - 0.011 } and n = 1.02 { +0.31 \atop - 0.10 } , and the Bayesian analysis gives values of \Omega = 0.98 { +0.14 \atop - 0.19 } , \Omega _ { B } h ^ { 2 } = 0.029 { +0.015 \atop - 0.010 } , and n = 1.18 { +0.10 \atop - 0.23 } , all at the 95 % confidence level .