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...

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):
32 46 47 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 =

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?
single mean
single proportion

(a) What is the level of significance?

State the null and alternate hypotheses.
H0: μ = 48; H1: μ ≠ 48
H0: μ = 48; H1: μ > 48

H0: p = 48; H1: p <>
H0: p = 48; H1: p ≠ 48
H0: μ = 48; H1: μ <>
H0: p = 48; H1: p > 48

(b) What sampling distribution will you use? What assumptions are you making?
The standard normal, 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 Student's t, 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.)