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The ALICE collaboration recently reported high-statistics $\bf p_t$ spectra from 5 TeV and 13 TeV p-p collisions with intent to determine the role of jets in high-multiplicity collisions. In the present study a two-component (soft + hard) model (TCM) of hadron production in p-p collisions is applied to ALICE $\bf p_t$ spectra. As in previous TCM studies of A-B collision systems jet and nonjet contributions to $\bf p_t$ spectra are accurately separated over the entire $\bf p_t$ acceptance. The statistical significance of data-model differences is established leading to insights concerning selection bias and spectrum model validity.