The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this 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) Are the reading and writing scores of each student independent of each other? yes, they are paired since each student has both a reading score and a writing score no, they are paired since each student has both a reading score and a writing score yes, because reading and writing are two different activities Correct (b) 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? Ho: μdiff = 0 Ha: μdiff ≠ 0 Ho: μdiff = 0 Ha: μdiff > 0 Ho: μdiff = 0 Ha: μdiff < 0 Correct (c) The average observed difference in scores is x̄read - 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? The test statistic is: Incorrect (please round to two decimal places) The p-value is: Incorrect (please round to four decimal places) The conclusion of the test is: Since p<α we fail to reject the null hypothesis Since p ≥ α we do not have enough evidence to reject the null hypothesis Since p<α we reject the null hypothesis and accept the alternative Since p ≥ α we accept the null hypothesis Since p ≥ α we reject the null hypothesis and accept the alternative Correct (d) What type of error might we have made? Explain what the error means in the context of the application. Fielding Error Type I Throwing Error Type II Correct (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. yes, because there is almost a 0% chance that average reading and writing scores are the same no, because we rejected the idea that average reading and writing scores are equal yes, because the evidence was not strong enough to suggest that average reading and writing scores differ no, because most people will not earn an average score of 0 on either exam
The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this 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) Are the reading and writing scores of each student independent of each other? yes, they are paired since each student has both a reading score and a writing score no, they are paired since each student has both a reading score and a writing score yes, because reading and writing are two different activities Correct (b) 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? Ho: μdiff = 0 Ha: μdiff ≠ 0 Ho: μdiff = 0 Ha: μdiff > 0 Ho: μdiff = 0 Ha: μdiff < 0 Correct (c) The average observed difference in scores is x̄read - 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? The test statistic is: Incorrect (please round to two decimal places) The p-value is: Incorrect (please round to four decimal places) The conclusion of the test is: Since p<α we fail to reject the null hypothesis Since p ≥ α we do not have enough evidence to reject the null hypothesis Since p<α we reject the null hypothesis and accept the alternative Since p ≥ α we accept the null hypothesis Since p ≥ α we reject the null hypothesis and accept the alternative Correct (d) What type of error might we have made? Explain what the error means in the context of the application. Fielding Error Type I Throwing Error Type II Correct (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. yes, because there is almost a 0% chance that average reading and writing scores are the same no, because we rejected the idea that average reading and writing scores are equal yes, because the evidence was not strong enough to suggest that average reading and writing scores differ no, because most people will not earn an average score of 0 on either exam
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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5.20 High School and Beyond, Part I: The National Center of Education Statistics conducted a survey of high school seniors, collecting test data on reading, writing, and several other subjects. Here we examine a simple random sample of 200 students from this 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) Are the reading and writing scores of each student independent of each other?
- yes, they are paired since each student has both a reading score and a writing score
- no, they are paired since each student has both a reading score and a writing score
- yes, because reading and writing are two different activities
(b) 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?
- Ho: μdiff = 0
Ha: μdiff ≠ 0 - Ho: μdiff = 0
Ha: μdiff > 0 - Ho: μdiff = 0
Ha: μdiff < 0
(c) The average observed difference in scores is x̄read - 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?
The test statistic is: Incorrect (please round to two decimal places)
The p-value is: Incorrect (please round to four decimal places)
The conclusion of the test is:
- Since p<α we fail to reject the null hypothesis
- Since p ≥ α we do not have enough evidence to reject the null hypothesis
- Since p<α we reject the null hypothesis and accept the alternative
- Since p ≥ α we accept the null hypothesis
- Since p ≥ α we reject the null hypothesis and accept the alternative
(d) What type of error might we have made? Explain what the error means in the context of the application.
- Fielding Error
- Type I
- Throwing Error
- Type II
(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.
- yes, because there is almost a 0% chance that average reading and writing scores are the same
- no, because we rejected the idea that average reading and writing scores are equal
- yes, because the evidence was not strong enough to suggest that average reading and writing scores differ
- no, because most people will not earn an average score of 0 on either exam
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