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{+0.26atop -0.19}, Omega_{rm B}h^2=0.026{+0.020atop -0.011} and n=1.02{+0.31atop -0.10}, and the Bayesian analysis gives values of Omega=0.98{+0.14atop -0.19}, Omega_{rm B}h^2=0.0.029{+0.015atop-0.010}, and $n=1.18{+0.10atop -0.23}$, all at the 95% confidence level.
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