The choice of January 1 as a starting date is arbitrary. The results might be different if we start on a different date. For each of the days January 2 through January 7, construct a data set starting with that date and containing every seventh day thereafter. Use each of these data sets to perform the analyses in Exercises 25 and 26. Do your conclusions change?

Data From Exercise 25:

Drop the dates in which the record high occurred more than once, and test the hypothesis in Exercise 22 again. Does your conclusion change?

Data From Exercise 22:

If a record high is equally likely to occur in any year of observation, the mean year in which a record is observed would occur at the midpoint of the observation period, which is \((1871+2020) / 2=1945.5\). Test the hypothesis that the mean year in which a record high occurred is 1945.5 against the alternative that it is greater. What do you conclude?

Data From Exercise 26:

Perform a hypothesis test on the record lows, after dropping dates on which the record low occurred more than once, in which the alternative hypothesis is that the mean year is less than 1945.5. What do you conclude?