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A researcher using a large and representative sample, establishes that (given sampling error) the 95% confidence interval of the Pearson correlation for SAT score and college GPA is .40 to .52 for the population of all SAT takers. The admissions adviser of College of the Arts finds that the observed correlation for that schools students is .30. What should he conclude? A. His students are different from the population of all SAT takers. B. His students represent the population of all SAT taker C. For students of the arts, scholastic aptitude doesn't matter much D. He can't conclude anything from this info.

For a two tailed test with alpha =.05, what is the decision for these data: r=.80, N=27? A. fail to reject the null B. Accept the null C. Reject the null D. we can't tell from this info
Submitted: 8 years ago.Category: Math Homework
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6/18/2010
Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago
Scott
Scott, MIT Graduate
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Hi there,

 

A researcher using a large and representative sample, establishes that (given sampling error) the 95% confidence interval of the Pearson correlation for SAT score and college GPA is .40 to .52 for the population of all SAT takers. The admissions adviser of College of the Arts finds that the observed correlation for that schools students is .30. What should he conclude? A. His students are different from the population of all SAT takers. B. His students represent the population of all SAT taker C. For students of the arts, scholastic aptitude doesn't matter much D. He can't conclude anything from this info.

 

Certainly not B, since it's outside the interval, and C is actually funny :)

The answer is:

A. His students are different from the population of all SAT takers.

 

For a two tailed test with alpha =.05, what is the decision for these data: r=.80, N=27? A. fail to reject the null B. Accept the null C. Reject the null D. we can't tell from this info

 

t = r*sqrt((n-2)/(1-r^2))

t = 0.8*sqrt((27-2)/(1-0.8^2))

t = 6.666

That's well above any critical value for any signficance level, especially 0.05!

So:

C. Reject the null

 

Let me know if you have any questions,

Scott

Scott
Scott, MIT Graduate
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Customer reply replied 8 years ago
That was my last one. THANK YOU!
Math Tutor or Teacher: Scott, MIT Graduate replied 8 years ago

Ok, have a great night!

-Scott

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