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In order to estimate the difference between the average Miles per Gallon of two different models...

In order to estimate the difference between the average Miles per Gallon of two different models of cars, samples are taken and the following information is collected.

Model A

Sample Size 16

Sample Mean 29

Sample Variance 16

Model B

Sample Size 18

Sample Mean 26

Sample Variance 9

Note: Assume that both populations are normally distributed.

  1. a) (16 points) Find a 95% confidence interval for the difference between the average Miles per Gallon for the two models.

  2. b) (4 points) From your answer in Part a), is there conclusive evidence that one model gets a significantly higher average MPG than the other? Why or why not? Explain.

please show all work neatly

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