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):
29 42 49 48 53 46 30 51 42 52
i. Use your calculator to verify that the mean age of a car when the fuel injection system fails is  = 44.2 months, with standard deviation s ≈ 8.61 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.
Are we testing a single mean or a single proportion? Assume underlying population distributions are mound-shaped and symmetrical for problems with small samples that involve testing a mean.
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.