You are in the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 24 domestic car makes and find an average fuel economy of 35.696 MPG with a standard deviation of 4.931 MPG. For imports, you sample 16 cars and find an average MPG of 34.345 MPG with a standard deviation of 7.118. If a 90% confidence interval is calculated to estimate the difference between the average fuel economy of domestic and import mid-size cars, what is the margin of error

Question

03-06-2021
Mathematics

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You are in the market for a new car. You want to check whether there is a significant difference between the fuel economy of mid-size domestic cars and mid-size import cars. You sample 24 domestic car makes and find an average fuel economy of 35.696 MPG with a standard deviation of 4.931 MPG. For imports, you sample 16 cars and find an average MPG of 34.345 MPG with a standard deviation of 7.118. If a 90% confidence interval is calculated to estimate the difference between the average fuel economy of domestic and import mid-size cars, what is the margin of error

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AbsorbingMan AbsorbingMan · Answer 1 · 2021-06-04T04:06:54+02:00

Solution :

It is given that the mean and the standard deviation for a sample of 24 domestic cars is 35.696 MPG and 4.931 MPG respectively and the mean and the standard deviation for a sample of 16 cars is 34.345 MPG and 7.118 respectively.

The 90% confidence level for the men difference between the two samples is (-2.906, 2.844).

We know that the confidence interval is calculated to determine the mean difference among the two samples with the specified level of confidence.

Therefore, we can say that with 90% confidence, we have the 90% chances that the true mean differences will be within the range of -2.906 MPG to 2.844 MPG.

Thus, it is required 90% confidence interval interpretation.