Methods are given for constructing, from past sample data, prediction intervals (i) to contain the ratio of the variances of future samples from two normal distributions and (ii) to contain the ratio of the means from future samples from two exponential distributions. Such intervals are required, for example, when a producer wishes to predict the results of a future test, to be conducted by a consumer or regulatory agency, to compare its product with a competitor's. A new tabulation of percentage points of the distribution of two independent F ratios to obtain such intervals is provided; this extends existing tabulations.