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):25 44 45 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 two decimal places.)x = monthss = 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?single meansingle proportion (a) What is the level of significance? State the null and alternate hypotheses._ H0: p = 48; H1: p > 48_ H0: p = 48; H1: p ? 48 _ H0: ? = 48; H1: ? > 48_ H0: p = 48; H1: p 0.250_ 0.125

Sketch the sampling distribution and show the area corresponding to the P- value. O -4 -4 (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