Question: Bill and Hillary got married and moved into a new house. Bill and Hillary want to analyze the difference between their population means. They took samples for 10 consecutive days. The sample based summaries are shown in the table below. Assume that individual commute time (in minutes) is normally distributed. Bill believes that the both populations share the same unknown common variance, and Hillary objected saying that she would prefer to assume entirely unknown variances. Table below presents the sample summaries derived from two independently collected samples.

1. What number of degrees of freedom will be assessed to the t-statistic by Hillary?
   (degrees of freedom by Hillary) =
2. What standard error will be assessed to the difference between two sample means by Hillary? Please write down the formula in either case! (se for Hillary) = ??
3. At the 1\% significance level, does Hillary have evidence that the population average commute time for bill was lower than that for Hillary? Hillary's decision is = ??
4. What critical values will Hillary use?
   (critical value for Hillary) = ??
5. Evaluate the test statistic.

(test statistic value for Hillary) = ??

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