1. Eagle Rock Oil claims their gasoline additive increases fuel economy. Fifteen identical vehicles were obtained and their mileage before treatment was recorded. Using identical conditions as much as possible, these vehicles were given the gasoline additive and their after-treatment mileage was then recorded. Run a hypothesis test, find p and state your conclusion whether Eagle Rock Oil's claim is true, using = 0.05. 3. Sonnets by a famous Elizabethan poet William Wordsmith are known to contain an average of = 8.6 new words (words not used in other works). The standard deviation of new words used in his works are = 2.9. A new manuscript of 8 new sonnets has been unearthed and the debate among scholars is about whether this William actually wrote them or not. The average use of new words for these 8 sonnets are x = 11.1. Using = 0.05 and statistical hypothesis testing, can we conclude that these are his work? Assume conditions of normality are met. Before Treatment After Treatment 23 25 16 21 32 28 21 25 20 25 28 25 12 15 19 18 35 31 20 26 20 24 26 29 18 21 29 24 27 25 2. Four different brands of alkaline batteries are being compared by testing them in different flashlights. The lifetimes of the batteries are measured and recorded below. Energizer Duracell Rayovac 27 31 24 Lifeline 26 35 24 29 36 30 31 28 38 25 38 23 26 27 32 24 31 Preliminary data indicates that all batteries come from normal populations. Is there a significant difference in lifetime of the different batteries at the 10% level? State your conclusions in the proper form. 4. What are the 3 ways that data can be checked to see if the normality conditions are being met for a group of sample means. List these in order of what should be checked first. 5. A study shows that the average 2-bedroom apartment in Eastern Idaho is $2295. The Rexburg Chamber of Commerce claims that their housing costs are in line with this claim. You are skeptical and survey 36 random apartments and find that x = $2440, s = $360. Using = 0.05, do you believe the Chamber of Commerce's claim or do you feel you are getting shafted? Run a hypothesis test, find the p-value and state your conclusion.