The manufacturer of a sports car claims that the fuel injection system lasts 48 months before it needs to be replaced. A consumer group tests this claim by surveying a random sample of 10 owners who had the fuel injection system replaced. The ages of the cars at the time of replacement were (in months): 21 48 41 48 53 46 30 51 42 52 LO USE SALT (i) Use your calculator to calculate the mean age of a car when the fuel injection system fails x and standard deviation s. (Round your answers to four decimal places.) X = months S = months (ii) Test the claim that the fuel injection system lasts less than an average of 48 months before needing replacement. Use a 5% level of significance. What are we testing in this problem? O single proportion O single mean (a) What is the level of significance? State the null and alternate hypotheses. O Ho: p = 48; H: p > 48 O Ho: p = 48; H1: p 48 (b) What sampling distribution will you use? What assumptions are you making? The standard normal, since we assume that x has a normal distribution with known o. The standard normal, since we assume that x has a normal distribution with unknown o. O The Student's t, since we assume that x has a normal distribution with known o. The Student's t, since we assume that x has a normal distribution with unknown o. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. O P-value > 0.250 O 0.125 0.250 O 0.125