Question

In: Statistics and Probability

In Born together—Reared apart: the Landmark Minnesota twin study (2012), Nancy Segal discusses the efforts of...

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?

Solutions

Expert Solution

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


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