2. Scientists collect a simple random sample of 25 menthol cigarettes and 25 nonmenthol cigarettes. Both samples consist of cigarettes that are filtered, 100 mm long and non-light. The menthol cigarettes have a mean nicotine amount of 0.87 mg and a standard deviation of 0.24 mg. The nonmenthol cigarettes have a mean nicotine amount of 0.92 mg and a standard deviation of 0.25 mg. Use a 0.05 significance level to test the claim that menthol cigarettes and nonmenthol cigarettes have different amounts of nicotine. Does menthol appear to have an effect on the nicotine content? a) State the Null and Alternative Hypotheses and define which variable is represented by 1 and 2 . [2 marks] b) State which test statistic we should use. (Don't worry about verifying that we've met all the requirements to use that test statistic - just assume we can). [1 mark] c) What are the critical value(s)? Sketch a graph and label the critical points. [2 mark] d) Calculate the calculated test statistic. [2 mark] e) Do we reject the null hypothesis? Why or why not? Explain. [2 marks] f) In the context of this question, what does our answer to part e mean? (For example, if we reject the null hypothesis, what does this mean about the daily travel expense