Hours of sleep

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Four students produced a 95% confidence interval 16.753\pm 7.39 hours for the mean hours slept over a weekend. What is the smallest sample size that would bring the margin of error down to 2 hours, keeping the same estimated standard deviation and the same normal approximation to the critical value?

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The pilot margin is 7.39=t_{3,\,0.975}\,s/\sqrt{4} with t_{3,\,0.975}\approx 3.182, so s\approx 4.65. A future sample of size n has margin t_{n-1,\,0.975}\,s/\sqrt n. The smallest n for which this is at most 2 is n=24: t_{23,\,0.975}\approx 2.07 and 2.07\times 4.65/\sqrt{24}\approx 1.96<2, while n=23 is just over 2.