In a study of student loans at four-year colleges across the US, the national average was...

  

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In a study of student loans at four-year colleges across the US, the national average was found to be $29,411. You are sure that your school has a lower average of the amount that students need to borrow to complete a degree at your school. You make a claim that a student can graduate with an average debt lower than the national average. To test your claim, you use data from a random sample of recent graduates from your school. The data is in the attached file. 1. At a = 0.05, is there enough evidence to support your claim? Be sure to show the following information: a. Null and alternative hypotheses in appropriate symbolic form b. Test statistic c. P-value. 2. For the hypotheses you specified, there are two errors that could occur: a. Concluding that the student loan average at your school is lower than the national average, when it is not. b. Concluding that the student loan average at your school is not lower than the national average, when it is. 3. Determine which of the above two errors is a Type I error and which is a Type II error. Indicate which error would have worse consequences and why. 4. How could the hypothesis test be conducted in order to reduce the chance of making the more serious error? 12345678 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Amount Borrowed 41685 36969 22518 23374 28298 19845 29501 32351 43035 25400 36368 31678 33266 30147 30895 30933 25687 30306 26564 24368 14208 28663 28281 33745 34679 23273 27283 35138 30256 16183 23629 13239 17167 21593 24961 31567 27611 33308 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 30949 30589 8784 22265 9124 31530 32515 23809 27286 28919 34057 31052 26937 31027 23435 32817 24378 E In a study of student loans at four-year colleges across the US, the national average was found to be $29,411. You are sure that your school has a lower average of the amount that students need to borrow to complete a degree at your school. You make a claim that a student can graduate with an average debt lower than the national average. To test your claim, you use data from a random sample of recent graduates from your school. The data is in the attached file. 1. At a = 0.05, is there enough evidence to support your claim? Be sure to show the following information: a. Null and alternative hypotheses in appropriate symbolic form b. Test statistic c. P-value. 2. For the hypotheses you specified, there are two errors that could occur: a. Concluding that the student loan average at your school is lower than the national average, when it is not. b. Concluding that the student loan average at your school is not lower than the national average, when it is. 3. Determine which of the above two errors is a Type I error and which is a Type II error. Indicate which error would have worse consequences and why. 4. How could the hypothesis test be conducted in order to reduce the chance of making the more serious error? 12345678 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 Amount Borrowed 41685 36969 22518 23374 28298 19845 29501 32351 43035 25400 36368 31678 33266 30147 30895 30933 25687 30306 26564 24368 14208 28663 28281 33745 34679 23273 27283 35138 30256 16183 23629 13239 17167 21593 24961 31567 27611 33308 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 30949 30589 8784 22265 9124 31530 32515 23809 27286 28919 34057 31052 26937 31027 23435 32817 24378 E

Answer rating: 100% (QA)

Answer 1 a Let X denote the amount that students need ... View the full answer