Question

In: Statistics and Probability

In Born Together – Reared Apart: The Landmark Minnesota Twin Study (2012), Nancy Segal discusses the...

  1. 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. Below are 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).
    1. What is the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings?
    2. 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
    3. 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 at a = .01. What is your conclusion?

No Siblings

With Siblings

Name

SAT Score

Name

SAT Score

Bob

440

Donald

420

Matthew

610

Ronald

540

Shannon

590

Kedriana

630

Tyler

390

Kevin

430

Michelle

410

Erin

460

Darius

430

Michael

490

Wilhelmina

510

Josephine

460

Donna

620

Jasmine

540

Drew

510

Kraig

460

Lucinda

680

Bernadette

650

Barry

580

Larry

450

Julie

610

Jennifer

640

Hannah

510

Diedra

460

Roger

630

Latishia

580

Garrett

570

Bart

490

Roger

630

Kara

640

Nancy

530

Rachel

560

Sam

590

Joey

610

Simon

500

Drew

520

Megan

610

Annie

640

Solutions

Expert Solution

using minitab>stat>basic stat>paired sample test

we have

Paired T-Test and CI: No sibling, siblings

Paired T for No sibling - siblings

N Mean StDev SE Mean
No sibling 20 547.5 82.5 18.4
siblings 20 533.5 80.1 17.9
Difference 20 14.0 53.7 12.0


90% CI for mean difference: (-6.8, 34.8)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 1.16 P-Value = 0.258

1 ) the mean difference between the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings is 14.0

2 ) 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 is (-6.8 ,34.8)

3 )let us consider u = no sibling - siblings

Ho : ud = 0

Ha: ud

the value of test stat is 1.16

p value is 0.258

since p value is greater than 0.01 so we do nit reject Ho and conclude that the critical reading SAT scores for the twins raised with no siblings and the twins raised with siblings at a = .01 is same


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