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 = 48 b. H0: μ = 48 Versus H1: μ < 48 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

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 = 48 b. H0: μ = 48 Versus H1: μ < 48 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

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Description: 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 consume

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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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

H0: μ < 48 Versus H1: μ = 48

H0: μ = 48 Versus H1: μ < 48

H0: μ = 48 Versus H1: μ ≠ 48

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

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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