6. Below is the data for subjects who were given a new pain medication to investigate the effect on pain tolerance. Higher scores represent higher tolerance. Subjects were given both a placebo and the new drug in random order. Participants were selected at random and pain tolerance is normally distributed in the population. Subject # 1 2 3 4 5 Mean SD New Pain 44 46 40 42 41 42.6 2.41 Drug Placebo 35 40 33 41 37 37.2 3.35 Differenc 5.4 3.05 es Perform the appropriate statistical test to see if the new pain medication has any effect on pain tolerance. Use a t-critical of 2.776. 7. For the following questions, identify what type of test is being conducted and write the appropriate null and alternative hypothesis. a. A professor wants to test whether students do better during finals if they chew gum than if they don't. He has half his class chew gum during an exam and half not chew gum. b. A running club wants to know if members run at different speeds on cold days and warm days. The group of 20 runners measures each of their run times on a 40 degree day and again on a 90 degree day. c. An undergrad at UT wants to know if her average commute to UT is significantly longer than 10 minutes. She measures her commute time for 15 days. d. A fruit grower wants to know if his trees bare significantly different amounts of fruit in drought years than non-drought years. He measures the amount of fruit produced by each of his trees for a drought harvest, and for a non-drought harvest