If there have been no temperature trends over the years, then it will be equally likely for the record high or the record low to be more recent. If there has been a warming trend, it might be more likely for the record high to be more recent. Let p be the probability that the record high occurred more recently than the record low. Use the sample proportion of dates where the high occurred more recently to test 110: p = 0.5 versus H1: p > 0.5. What do you conclude?
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