Question

In: Statistics and Probability

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before...

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 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 proportion single mean (a) What is the level of significance? State the null and alternate hypotheses. H0: μ = 48; H1: μ < 48 H0: p = 48; H1: p ≠ 48 H0: μ = 48; H1: μ ≠ 48 H0: μ = 48; H1: μ > 48 H0: p = 48; H1: p > 48 H0: p = 48; H1: p < 48 (b) What sampling distribution will you use? What assumptions are you making? The Student's t, 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 known σ. The standard normal, since we assume that x has a normal distribution with unknown σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.250 0.125 < P-value < 0.250 0.050 < P-value < 0.125 0.025 < P-value < 0.050 0.005 < P-value < 0.025 P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot (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 α? At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 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. There is sufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months. There is insufficient evidence at the 0.05 level to conclude that the injection system lasts less than an average of 48 months.

Solutions

Expert Solution


Related Solutions

The manufacturer of a sports car claims that the fuel injection system lasts 48 months before...
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): 27 46 49 48 53 46 30 51 42 52 What is the value of the sample test statistic? (Round your answer to three decimal...
The manufacturer of a sports car claims that the fuel injection system lasts 48 months before...
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): 23 44 45 48 53 46 30 51 42 52 (i) Use your calculator to calculate the mean age of a car when the fuel...
The manufacturer of a sports car claims that the fuel injection system lasts 48 months before...
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): 21 42 43 48 53 46 30 51 42 52 Use the sample data to calculate the mean age of a car when the fuel...
The manufacturer of a sports car claims that the fuel injection system lasts 48 months before...
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): 27 46 47 48 53 46 30 51 42 52 (i) Use your calculator to calculate the mean age of a car when the fuel...
The car manufacturer Lamborghini claims that its high-performance sports car, the Lamborghini Aventador, has an average...
The car manufacturer Lamborghini claims that its high-performance sports car, the Lamborghini Aventador, has an average top speed exceeding 220 mph. A car enthusiast tests this claim by renting 14 of the vehicles and recording their top speed. He finds that the average top speed of the sample is 218mph, with a sample standard deviation of 3mph. For the test, the car enthusiast determines that α = 0.10 Write the null and alternative hypotheses. Is this a left, right, or...
5. Suppose that a car manufacturer claims that its fuel efficiency (as measured in miles per...
5. Suppose that a car manufacturer claims that its fuel efficiency (as measured in miles per gallon) per tankful of gasoline follows a normal distribution with mean 35 mpg and standard deviation 2.0 mpg. a) What percentage of tankfuls would obtain between 30 and 40 mpg? (A table of standard normal probabilities appears at the end of this exam.) b) Would the percentage of tankfuls that obtain between 30 and 40 mpg be larger, smaller, or the same if the...
A new fuel injection system has been engineered for pickup trucks. The new system and the...
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 31 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...
A new fuel injection system has been engineered for pickup trucks. The new system and the...
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...
A new fuel injection system has been engineered for pickup trucks. The new system and the...
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...
A new fuel injection system has been engineered for pickup trucks. The new system and the...
A new fuel injection system has been engineered for pickup trucks. The new system and the old system both produce about the same average miles per gallon. However, engineers question which system (old or new) will give better consistency in fuel consumption (miles per gallon) under a variety of driving conditions. A random sample of 41 trucks were fitted with the new fuel injection system and driven under different conditions. For these trucks, the sample variance of gasoline consumption was...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT