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): 23 42 43 48 53 46 30 51 42 52 (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 = S= months 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? Osingle mean O single proportion (a) What is the level of significance? State the null and alternate hypotheses. Ho P = 48; H₁: p < 48 © Ho R = 48; H: "#48 OH = 48; H₁: < 48 Hop = 48; H₁: > 8 H₁ = 48; H₁: >48 OH P = 48; H₁: P + 48 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, since we assume that x has a normal distribution with known σ. The Student's t, since we assume that x has a normal distribution with unknown σ. The standard normal, since we assume that x has a normal distribution with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value>0.250 0.125 P-value < 0.250 0.050 P-value < 0.125 0.025 < P-value < 0.050 0.005 P-value < 0.025 P-value <0.005 Sketch the sampling distribution and show the area corresponding to the P-value. -2 2 -2 0 2 -2 2 -2 0 2 WebAssign Plot