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): 33 42 47 48 53 46 30 51 42 52 (1) 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 two 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 mean O single proportion (a) What is the level of significance? State the null and alternate hypotheses. O Ho: p = 48; H1: p # 48 O Ho: H = 48; H1: H > 48 O Ho: M = 48; H1: A 48 O Ho: M = 48; H1: p # 48(b) What sampling distribution will you use? What assumptions are you making? O The Student's t, since we assume that x has a normal distribution with unknown o. O The standard normal, since we assume that x has a normal distribution with known a. The Student's t, since we assume that x has a normal distribution with known a. O The standard normal, 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 the P-value. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value. O -4 -2 0 2 O -4 -2 0 2 -2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.(e) Interpret your conclusion in the context of the application. O There is sufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months. O There is insufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months