In: Statistics and Probability
In Born together—Reared apart: the Landmark Minnesota twin study (2012), Nancy Segal discusses the efforts of research psychologists at the University of Minnesota to understand similarities and differences between twins by studying sets of twins who were raised separately. The Excel Online file below contains critical reading SAT scores for several pairs of identical twins (twins who share all of their genes), one of whom was raised in a family with no other children (no siblings) and one of whom was raised in a family with other children (with siblings). Construct a spreadsheet to answer the following questions.
SAT Score No Siblings | SAT Score With Siblings | Change in SAT Scores (di) |
409 | 422 | -13 |
620 | 544 | 76 |
609 | 601 | 8 |
408 | 452 | -44 |
383 | 464 | -81 |
401 | 535 | -134 |
520 | 483 | 37 |
663 | 589 | 74 |
484 | 444 | 40 |
676 | 627 | 49 |
613 | 439 | 174 |
576 | 651 | -75 |
512 | 478 | 34 |
601 | 548 | 53 |
520 | 540 | -20 |
631 | 666 | -35 |
525 | 590 | -65 |
545 | 617 | -72 |
471 | 533 | -62 |
597 | 669 | -72 |
A) What is the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings? (to 2 decimals)
B) Provide a 90% confidence interval estimate of the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings. (to 2 decimals)
C) Conduct a hypothesis test of equality of the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings.
P-Value = ? (to 4 decimals)
At alpha = .01 what is your conclusion?
Can/Cannot we conclude that there is a difference between the mean scores for the no sibling and with sibling groups?
Solution:
A) What is the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings? (to 2 decimals)
Answer:
B) Provide a 90% confidence interval estimate of the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings. (to 2 decimals)
Answer: The 90% confidence interval estimate of the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings is:
C) Conduct a hypothesis test of equality of the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings.
P-Value = ? (to 4 decimals)
The p-value is:
Now using the excel function:
At alpha = .01 what is your conclusion?
Cannot we conclude that there is a difference between the mean scores for the no sibling and with sibling groups