Professor Neil is interested in determining whether viewing different colors affects subjects' mental states in a way that alters their athletic ability. As a part of her research she carries out the following experiment. Each subject is randomly assigned to wait in one of two rooms: a room in which all of the walls have been painted pink or another in which all of the walls have been painted red. After waiting for ve minutes, each subject is taken to a track and asked to run a 5K as fast as possible. Using the data from this experiment, Professor Neil carries out a statistical test of the null hypothesis that the population mean 5K time is equal across groups (those who waited in the pink room versus those who waited in the red room). Testing at the 1% level, she nds a statistically signicant difference. For each of the following, answer True or False. If false, explain. 1. The p-value for the null hypothesis that population means are equal across groups is greater than 0.01. 2. Professor Neil would also have found a statistically signicant difference had she carried out her test at the 5% level. 3. If there were really no difference in population means across the two groups, the chance of observing a test statistic at least as extreme as that observed by Professor Neil would be 0.01 or less. 4. Professor Neil's ndings have important practical implications for sports regulatory organizations such as the International Olympic Committee: all locker rooms should be painted exactly the same color to keep from throwing off the outcomes of sporting events