Ex: Phillip is interested in testing whether there are any difference between the life of long-lasting batteries and regular batteries. He and his brother independently did some research. They randomly picked some batteries from the packs they bought and tested their life. The results are (Sample size -- Mean -- Standard Deviation) Long lasting: 12 -- 49.2 -- 7.31 Regular: 10 -- 41.1 -- 6.40 a. Construct a 95% Confidence Interval of the difference of the average battery lives between the two batteries types. b. Use 0.05 significance level to set up the hypothesis testing and explain your results (is there an advantage for spending more on the long-lasting battery type?). c. What is your p-value here? d. What assumptions did you use in the hypothesis test? ***Also consider: can you reach the same conclusion by using the confidence interval in long-lasting batteries above or by using the hypothesis test in regular? Why?