Question 6 1S POINTS A sample of 20 first-year U.S. college students\' SAT score

Question

Question 6 1S POINTS A sample of 20 first-year U.S. college students' SAT scores from the Excel Correlation Analysis for the students of their SAT scores was collected. Below is the outpa performances on the Verhal and Math pams Verbal Math Verbal 1,0000 Math 0.7490 1.0000 1) How wou studemu ribe the asociation betwen the Verhal and Meath pats of s student's SAT (Le. for all 95% the first-year college students in the U.S)? Explain your reason by assuming s confidence level. 1 3pt] 2) Does the association you identified in the above part 1) exist in the population(

Explanation / Answer

Part 1

The given correlation analysis shows that the correlation coefficient, r, between the two SAT scores is 0.749. This suggests that 56% (r2 = 0.5610) of the variation in scores of one subject is explained by the variation in the score of the other subject. This, in effect, implies that the relationship between the two scores is fairly strong.   ANSWER   

[Note: r = 0.749 only suggests that the relationship between the two scores is fairly strong. But, it is not possible to say at this stage which score impacts which score. That can be answered only by a regression analysis.]

Part 2

The sample correlation of 0.749 is fairly high. Whether this would imply that the population correlation, , is also high would be revealed only by the following significance test.

Null hypothesis: H0: = 0 Vs Alternative H1: 0

Test statistic:

t = r/{(1 – r2)/(n - 2)}

= 0.749/(0.438999/18)

= 0.749/0.024389

= 0.749/0.1562

  = 4.796

Under H0, t ~ tn – 2

Rejection region, tcal > t crit

t crit = t18, 0.025 = 2.101 [from standard Statistical Tables]

Since tcal > t crit, H0 is rejected => the population correlation is significant.

Thus, there is evidence to suggest that among all the SAT aspirants there would be positive relationship between the SAT scores of Verbal and Math.

DONE

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