The results of a study of 255 students who paid a private

The results of a study of 255 students who paid a private classto help them improve their scores on a standardized test are shownbelow. The changes in both the Mathematics and Verbal scores forthese students are reproduced in the table. Complete parts athrough c below. a. Construct and interpret a 95% confidence interval for thepopulation mean change in the Mathematics score for students whopay a private class. Interpret this interval. Choose the correct answer below. A.One can be 95% confident the true mean change in theMathematics score lies within the above interval. B.One can be 95% confident the true mean change in theMathematics score is one of the end points of the aboveinterval. C.There is a 95% probability that the true mean change in theMathematics score is the mean of the interval. D.One can be 95% confident the true mean change in theMathematics score lies at the mean of the above interval. b. Construct and interpret a 95% confidenceinterval for the population mean change in the Verbal score forstudents who pay a private class. Interpret this interval. Choose the correct answer below. A.There is a 95% probability that the true mean change in theVerbal score is the mean of the interval. B.One can be 95% confident the true mean change in the Verbalscore is one of the end points of the above interval. C.One can be 95% confident the true mean change in the Verbalscore lies within the above interval. D.One can be 95% confident the true mean change in the Verbalscore lies at the mean of the above interval. c. Suppose the true population mean change inscore on one of the standardized tests for all students who paid aprivate class is 5. Which of the two tests, Mathematics or Verbal,is most likely to have this mean change? Explain. Choose the correct answer below. A.Mathematics is more likely to have this true mean changebecause it falls outside the 95% confidence interval forMathematics. B.Verbal is more likely to have this true mean change because itfalls within the 95% confidence interval for Verbal. C.Mathematics is more likely to have this true mean changebecause it falls within the 95% confidence interval forMathematics. D.Verbal is more likely to have this true mean change because itfalls outside the 95% confidence interval for Verbal. E.Both are equally likely to have this true mean change becauseit falls within the 95% confidence interval for both Verbal andMath. Attached