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Health-monitoring technologies for automatically detecting the early signs of Alzheimer's disease (AD) have become increasingly important. Speech responses to neuropsychological tasks have been used for quantifying changes resulting from AD and differentiating AD and mild cognitive impairment (MCI) from cognitively normal (CN). However, whether and how other types of speech tasks with less burden on older adults could be used for detecting early signs of AD remains unexplored. In this study, we developed a tablet-based application and compared speech responses to daily life questions with those to neuropsychological tasks in terms of differentiating MCI from CN. We found that in daily life questions, around 80% of speech features showing significant differences between CN and MCI overlapped those showing significant differences in both our study and other studies using neuropsychological tasks, but the number of significantly different features as well as their effect sizes from life questions decreased compared with those from neuropsychological tasks. On the other hand, the results of classification models for detecting MCI by using the speech features showed that daily life questions could achieve high accuracy, i.e., 86.4%, comparable to neuropsychological tasks by using eight questions against all five neuropsychological tasks. Our results indicate that, while daily life questions may elicit weaker but statistically discernable differences in speech responses resulting from MCI than neuropsychological tasks, combining them could be useful for detecting MCI with comparable performance to using neuropsychological tasks, which could help develop health-monitoring technologies for early detection of AD in a less burdensome manner.