Problem 7) A car manufacturer claims that the mean number of miles per gallon for the car manufactured by the company is more than 70. To test the claim a researcher measures the number of miles per gallon of each of a random sample of 20 cars and obtained sample mean of 71.2 and standard deviation 3.4. The number of miles per gallon may be assumed to be normally distributed. a) State the hypotheses and test the car manufacturer's claim using rejection regions. Use 1% level of significance, Le, a 0.01. (Show work). State Null and Alternative Hypotheses (2 points): Obtain Critical value(s) (2 points) (Round your answer to 3 decimal places).: Obtain Test Statistic (2 points) (Round your answer to 2 decimal places).: Interpretation and Conclusion: Circle only one (1 point) i) Reject the null hypothesis ii) Fail to reject the null hypothesis Why? (2 points) Is there enough evidence to support the car manufacturer's claim? Circle only one (1 point): i) Yes, there is enough evidence at a = 0.01 to support the manufacturer's claim ii) No, there is not enough evidence at a =0.01 to support the manufacturer's claim b) Obtain the P-value for the test above (4 points). (Round your answer to 2 decimal places). (Show work).