The manufacturer of a sports car claims that the fuel injection system lasts at least 48 months before it needs to be replaced. A consumer group does not believe this claim. The consumer group...





The manufacturer of a sports car claims that the fuel injection system lasts at least 48 months before it needs to be replaced. A consumer group does not believe this claim. The consumer group believes that it must be less than 48 months. The consumer group tests th the​ manufacturer's claim by surveying a random sample of 15 sports car
owners

who had the fuel injection system replaced. The ages of sports cars at the time of replacement were​ (in months) as​ follows: Assume that that the age of sports cars at the time of replacement is normally distributed.


29 42 49 48 53 46 30 51 42 52 38 47 50 34 52



Read ​ part-a through​ part-f of this question fully and do them please. In your​ answers, please keep the appropriate number of decimals as requested in each part of the question.





A. Compute the mean and the standard deviation of the above sample
data.

Be sure to find the appropriate standard deviation for purposes of carrying out the hypothesis test of interest.


a. Sample Mean​ =Round to 1 decimal place please


a. Sample Standard Deviation​ =

Round to 4 decimal places please.




B. Use the above sample data to find a ​95% confidence interval

for the population mean number of months a fuel injection system lasts before it needs replacement.


The​ 95% confidence interval for mean number of months a fuel injection system lasts before it needs replacement is


​a. (_,_​) Round to 3 decimal places please



C. State the null and alternate hypotheses that would be used to test the consumer​ group's suspicion that the fuel injection system lasts less than 48 months before it needs to be replaced







a.


​H0: μ​ < 48="" versus​ h1:="" μ="" ​ ="">







b.


​H0: μ​ = 48 Versus​ H1: μ​ <>







c.


​H0: μ​ = 48 Versus​ H1: μ​ ≠ 48







d.


​H0: μ​ = 48 Versus​ H1: μ​ > 48








D. Continuing part​ (c), find the​ p-value of the appropriate test and decide whether or not to reject the null hypothesis at the​ 5% significance level.


a. ​P-value =

Round to 4 decimal places.


b. Based on​ 5% level of​ significance, your final conclusion​ is:









Reject the null hypothesis OR





Fail to reject the null hypothesis







E.

Does the​ manufacturer’s claim appear to be​ plausible? That​ is, did you find sufficient sample evidence to support the​ manufacturer’s claim?









a. ​YES, There is a significant evidence that the fuel injection system lasts at least 48 months before it needs to be replaced








​b. NO, There is NO significant evidence that the fuel injection system lasts at least 48 months before it needs to be replaced








F.   What type of error is possible with your final decision about the null hypothesis in part​ (d).








a. A type I error








b. A type II error





















Jun 07, 2022
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