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A survey of high school seniors was conducted by the National Center of Education Statistics. They were collecting test data on reading, writing, and several other subjects. A random sample of 250 students was examined from the survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. (a) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? (b) Check the conditions required to complete this test. (c) The average observed difference in scores is and Tread-write=-0.545,, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? o Calculate the T-test. o Calculate the degrees of freedom. o Given the p-value of 0.39, provide the conclusion.

A survey of high school seniors was conducted by the National Center of Education Statistics. They were collecting test data on reading, writing, and several other subjects. A random sample of 250 students was examined from the survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. (a) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? (b) Check the conditions required to complete this test. (c) The average observed difference in scores is and Tread-write=-0.545,, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? o Calculate the T-test. o Calculate the degrees of freedom. o Given the p-value of 0.39, provide the conclusion.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.3: Conditional Probability; Independent Events; Bayes' Theorem
Problem 27E: Another friend asks you to explain how to tell whether two events are dependent or independent. How...
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(d) What type of error might we have made? Explain what the error means in the context of the application. (e) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning.
Transcribed Image Text:(d) What type of error might we have made? Explain what the error means in the context of the application. (e) Based on the results of this hypothesis test, would you expect a confidence interval for the average difference between the reading and writing scores to include 0? Explain your reasoning.
Part 1 A survey of high school seniors was conducted by the National Center of Education Statistics. They were collecting test data on reading, writing, and several other subjects. A random sample of 250 students was examined from the survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. (a) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? (b) Check the conditions required to complete this test. (c) The average observed difference in scores is and Tread-write=-0.545,, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? o Calculate the T-test. Calculate the degrees of freedom. o Given the p-value of 0.39, provide the conclusion.
Transcribed Image Text:Part 1 A survey of high school seniors was conducted by the National Center of Education Statistics. They were collecting test data on reading, writing, and several other subjects. A random sample of 250 students was examined from the survey. Side-by-side box plots of reading and writing scores as well as a histogram of the differences in scores are shown below. (a) Create hypotheses appropriate for the following research question: is there an evident difference in the average scores of students in the reading and writing exam? (b) Check the conditions required to complete this test. (c) The average observed difference in scores is and Tread-write=-0.545,, and the standard deviation of the differences is 8.887 points. Do these data provide convincing evidence of a difference between the average scores on the two exams? o Calculate the T-test. Calculate the degrees of freedom. o Given the p-value of 0.39, provide the conclusion.
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