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.
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: _________ (please round to two decimal places)
The p-value is: ___________ (please round to four decimal places)
The conclusion of the test is:
- ( )Since p ≥ α we accept the null hypothesis
- ( )Since p ≥ α we reject the null hypothesis and accept the alternative
- ( )Since p ≥ α we do not have enough evidence to reject the null hypothesis
- ( )Since p<α we fail to reject the null hypothesis
- ( )Since p<α we reject the null hypothesis and accept the alternative
(a)
From the given information, a simple random sample of 200 students from this survey of high school seniors, collecting test data on reading, writing, and several other subjects.
It is clear that the data is collected on each student which indicates reading score and writing score for same student.
Correct Answer: No, they are paired since each student has both a reading score and a writing score.
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