The results of a study of 264 students who paid a private tutor to help them imp
ID: 3064361 • Letter: T
Question
The results of a study of 264 students who paid a private tutor to help them improve their scores on a standardized test are shown below. The changes in both the Mathematics and Verbal scores for these students are reproduced in the table. Complete parts a through c below.
Test score improvements
Math
Verbal
Mean change in score
17
7
Standard deviation of score changes
66
48
a. Construct and interpret a 95% confidence interval for the population mean change in the Mathematics score for students who pay a private tutor. ( , )
Interpret this interval. Choose the correct answer below.
A. One can be 95% confident the true mean change in the Mathematics score lies at the mean of the above interval.
B. One can be 95% confident the true mean change in the Mathematics score lies within the above interval.
C. One can be 95% confident the true mean change in the Mathematics score is one of the end points of the above interval.
D. There is a 95% probability that the true mean change in the Mathematics score is the mean of the interval.
b. Construct and interpret a 95% confidence interval for the population mean change in the Verbal score for students who pay a private tutor.
Interpret this interval. Choose the correct answer below.
A. One can be 95% confident the true mean change in the Verbal score is one of the end points of the above interval.
B. One can be 95% confident the true mean change in the Verbal score lies within the above interval.
C. There is a 95% probability that the true mean change in the Verbal score is the mean of the interval.
D. One can be 95% confident the true mean change in the Verbal score lies at the mean of the above interval.
c. Suppose the true population mean change in score on one of the standardized tests for all students who paid a private tuttor is 55.
Which of the two tests, Mathematics or Verbal, is most likely to have this mean change? Explain.
Choose the correct answer below.
A. Verbal is more likely to have this true mean change because it falls within the 95% confidence interval forVerbal
B. Mathematics is more likely to have this true mean change because it falls within the 95% confidence interval for Mathematics.
C.Verbalis more likely to have this true mean change because it falls outside the 95% confidence interval for Verbal
D. Mathematics is more likely to have this true mean change because it falls outside the 95% confidence interval for Mathematics.
E- Both are equally likely to have this true mean change because it falls within the 95% confidence interval for both Verbal and Math.
Test score improvements
Math
Verbal
Mean change in score
17
7
Standard deviation of score changes
66
48
Explanation / Answer
a)
Option B. One can be 95% confident the true mean change in the Mathematics score lies within the above interval.
b)
Option B: One can be 95% confident the true mean change in the Verbal score lies within the above interval.
CI for 95% n 264 mean 17 z-value of 95% CI 1.9600 std. dev. 66 SE = std.dev./sqrt(n) 4.06202 ME = z*SE 7.96141 Lower Limit = Mean - ME 9.03859 Upper Limit = Mean + ME 24.96141 95% CI (9.0386 , 24.9614 )Related Questions
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