8. (5 points) In statistics, there is a principle that \"correlation between two variables does not necessarily mean there is a causal connection between the two variables.\" Which of the following statements are true and which are false? Choose the correct answer. (a) Ifthere is no causal connection between two variables, there may be a correlation between the two variables. (T or F) (b) Ifthere is a causal connection between two variables, there will be a correlation between the two variables. (T or F) (c) Ifthere is a correlation between two variables, there will always be a causal connection between the two. (T or F) (d) Ifthere is no correlation between two variables, there will always be a causal connection between the two. (T or F) (e) Give a reason why two variables which are not causally connected might appear to be strongly correlated with each other. 9. (5 points) Given the statement: Theory A predicts effect B. Which of the following 4 statements will always be true? (a) I see effect B, therefore theory A is true (b) I see effect ; therefore theory A is false. (c) I do not see effect B, therefore theory A is true (d) I do not see effect B, therefore theory A is false. 10. (10 points) This is a \"think\" problem. When using math, it is always good to know what the approximate answer will be before doing the problem. In this way, you will know if your calculated answer at least hasthem; of being correct. Two trains are heading towards each other on the same track. They are initially 100 miles apart and are travelling at 50 mi/hr. There is a superfast bee who can y at 200 mifhr The the front of the other train. The bee travels back and forth until the trains collide. Estimate (in miles) how far the bee will travel until the trains collide. Be sure to give your reasoning for your estimate