A researcher wanted to investigate a person's performance after suffering from sleep deprivation, with two types of people who suffer from insomnia. In group one, 40 people were allowed to sleep for five hours, in group two, 35 people were given three hours. Then performance was measured by performing a memory test with a standard population deviation of 6 people in each group and assumed normal distribution. The average memory test score in the group that slept three hours was 58; in the five-hour group, it was 62.

a)If researchers are interested in testing whether memory performance has significant differences in both groups, explain the zero hypothesis and its alternative hypotheses and test the hypotheses with an alpha level of 0.01. What's the conclusion of the researchers?

b) If researchers are interested in researching whether more sleep can deliver better performance? Test the hypothesis at an alpha level of 0.05. What's the conclusion of the researchers?