A popular car manufacturing brand claims that their car model Rex500 has an average highway mileage of 21.50 Km/L, you want to test whether this claim is statistically significant or not.You managed to get data from 45 cars of this model and found that the average highway mileage is 20.42 Km/L, with a standard deviation of 2.7 Km/LWith 99% confidence, will you be able to conclude that the average highway mileage is statistically lower than the claimed fuel economy?Use the appropriate test and select the correct option below:
Question
A popular car manufacturing brand claims that their car model Rex500 has an average highway mileage of 21.50 Km/L, you want to test whether this claim is statistically significant or not.You managed to get data from 45 cars of this model and found that the average highway mileage is 20.42 Km/L, with a standard deviation of 2.7 Km/LWith 99% confidence, will you be able to conclude that the average highway mileage is statistically lower than the claimed fuel economy?Use the appropriate test and select the correct option below:
Solution
To test the claim, we can use a one-sample t-test. The null hypothesis (H0) is that the average highway mileage is equal to the claimed fuel economy (21.50 Km/L), and the alternative hypothesis (H1) is that the average highway mileage is less than the claimed fuel economy.
Here are the steps to perform the test:
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Calculate the t-statistic: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)) t = (20.42 - 21.50) / (2.7 / sqrt(45)) t = -1.08 / 0.40 t = -2.7
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Determine the degrees of freedom, which is the sample size minus 1: df = 45 - 1 = 44.
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Look up the critical t-value for a one-tailed test at the 99% confidence level with 44 degrees of freedom. The critical t-value is -2.69.
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Compare the calculated t-statistic with the critical t-value. If the calculated t-statistic is less than the critical t-value, we reject the null hypothesis.
In this case, the calculated t-statistic (-2.7) is less than the critical t-value (-2.69), so we reject the null hypothesis. This means that we can conclude with 99% confidence that the average highway mileage is statistically lower than the claimed fuel economy.
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