Question

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 30.753 MPG with a standard deviation of 3.494 MPG. For imports, you sample 10 cars and find an average MPG of 30.784 MPG with a standard deviation of 6.412. You use this information to calculate a 90% confidence interval for the difference in mean fuel economy of (-2.906, 2.844). Of the following statements, what is the best interpretation of this interval?

Answer 1

It i given that the mean and standard deviation for a sample of 24 cars is 30.753 MPG and 3.494 MPG and the mean and standard deviation for a sample of 10 cars is 30.784 MPG and 6.412 MPG.

90% confidence interval for the mean difference between the two samples is (-2.906, 2.844)

we know that confidence interval is calculated to find the mean difference between the two samples with specified level of confidence.

So, we can conclude that with 90% confidence, we have 90% chances that the true mean difference will be within the range of -2.906 MPG to 2.844 MPG

This is the required 90% confidence interval interpretation.