Question

14. The boxplots below summarize the distributions of SAT verbal and math scores among students at an upstate New York high school: Boxplot of Hath, verbal so ... The Which of the following statements is false? A. The range of the math scores equals the range of the verbal scores B. The highest math score equals the median verbal score. The verbal scores are roughly symmetric while the math scores are skewed to the left. D. The interquartile range for the math scores is larger than the interquartile range for the verbal scores 15. Pre-study scores versus post-study scores for a class of 120 college freshman English students were considered. The residual plot for the least squares regression line showed no pattern. The least squares regression line was 0.2+0.9x with a correlation coefficient r0.68. What percent of the variation of post-study scores can be explained by the variation in pre-study scores? A. 68.0% B. 82.5% C. 32.0% D. 46.2% E. We cannot determine the answer using the information given 16. Ir P(A) 0.2 and P(B) -0.4, what is P(A or B) if A and B are independent? A. 0.6 0.0.08 D. 0.52 E. None of these CO 17. If PA) -0.2 and P(B) -0.4, what is P(A or B) if A and B are disjoint? A. 0.6 B. 0.08 C.O D.0.52 E. None of these

Answer 1

14

Range = maximum value – minimum value

Range of the math scores = 600 – 300 =300

Range of the verbal scores =750 – 450 = 300

So, the range of the math scores equal the range of the verbal score.

The highest math score = 600

Median of verbal score = 600

So, the highest math score equals the median verbal score.

In the given boxplot of math score, we see that the left side line is longer than right side line. It means the math score are skewed to the left.

And in the given boxplot of verbal scores, left side line and right side line are almost equal and line within the box is roughly centered. It means roughly symmetric.

So, the verbal scores are roughly symmetric while the math scores are skewed to the left.

Interquartile range = Third quartile (Q3) - First quartile (Q1)

Interquartile range for math score = 550 – 425 = 125

Interquartile range for verbal score = 680 – 525 = 155

So, the interquartile range of verbal scores is larger than the interquartile range for the math scores.

Therefore, the false statement is option   D.

15)

Correlation coefficient (r) measures the strength and direction of the linear relationship between two variables.

Given

Correlation coefficient (r) = 0.68

It means 68% of the variation of post-study scores can be explained by the variation in pre-study scores.

Therefore, the correct option is A. 68%

16)

If A and B are independent then

P(A or B) = P(A) + P(B) – P(A)*P(B)

Given

P(A)=0.2

P(B)=0.4

Now

P(A or B) = 0.2 + 0.4 –( 0.2*0.4)

                = 0.6 – 0.08

                = 0.52

Therefore, the correct option is D. 0.52

17)

If A and B are disjoint then

P(A or B) = P(A) + P(B)

Given

P(A)=0.2

P(B)=0.4

Now

P(A or B) = P(A) + P(B) =0.2 + 0.4 = 0.6.

Therefore, the correct option is A. 0.6