  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_{\rm 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_{\rm B}h^2=0.0.029{+0.015\atop-0.010},
and $n=1.18{+0.10\atop -0.23}$, all at the 95% confidence level.
