Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 90

What is the level of significance State the null and alternate hypothesis.
(b) Check Requirements 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 answer in parts (a) to (c), will you reject or fail to reject the null hypothesis Are the data statistically significant at level
(e) Interpret your conclusion in the context of the application. Note: For degrees of freedom d.f. not in the Student's t table, use the closest d.f. that smaller. In some situations, this choice of d.f. may increase the P -value by a small amount and therefore produce a slightly more "conservative" answer. Answers may vary due to rounding.
Sports Car: Fuel Injection 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.