3. HeartSense CEO Lex Luthor caught word of the preliminary findings of the heartworm study and knew that a non- significant finding would cost his company millions of dollars. His marketing director Lena (who is very knowledgeable in statistics) told him to simply increase his sample size and have the United States National Veterinary Associates re-run the analyses with this greater sample size. The NVA agreed and found the following figures: (x-bar/M= 21.51, s=4.1) for their sample of 101 (n=101), the national average is still the same (u=22.60). Lex was nervous since their sample mean increased, but Lena told him not to worry. a) What is your t-critical score (pay attention to the direction, should it be positive or negative)? (2pts) b) Compute standard error (2pts) c) Run a t-test to discern if you reject or retain your null hypothesis (4 pts) d) Did HeartSense get cleared for a national roll out? (2 pts) e) Explain what the difference between questions 1 and question 2's results. Why was the test significant even though the mean difference decreased? (4 pts) f) What does this tell us about a potential issue with t- tests? (4 pts)