Confidence intervals are useful tools for statistical decision-making purposes. In case of incomplete and vague data, fuzzy confidence intervals can be used for decision making under uncertainty. In this paper, we develop interval-valued intuitionistic fuzzy (IVIF) confidence intervals for population mean, population proportion, differences in means of two populations, and differences in proportions of two populations. The developed IVIF intervals can be used in cases of both finite and infinite population sizes. The developed fuzzy confidence intervals are equivalent decision-making tools to fuzzy hypothesis tests. We apply the proposed confidence intervals to the differences in the mean lives and failure proportions of two types of radiators used in automobiles, and a sensitivity analysis is given to check the robustness of the decisions.