Question

A researcher was interested in how students’ Graduate Record Examinations scores (GREQ- Quantitative and GREV-Verbal) predict college students’ graduate school Grade Point Average (GGPA). He collects data from 30 college students. The GRE Quantitative (X1) and GRE Verbal (X2) scores can range from 400-1600 (Note. This is the old GRE score scale). GGPA (Y) can range from 0.00 to 4.00.

f. What proportion of variance in graduate grade point average cannot be accounted by the variability in the quantitative GRE and verbal GRE scores in combination? In other words, what is the unexplained variation in the regression model. (6 p)

g. Is this proportion of variance statistically significant at the .05 level of significance? Justify your answer. This includes providing the parameter being estimated, the statistical test (F, t, etc.) and its value, degrees of freedom associated with the statistical test. (14 p)

h. Using an alpha level of .05, justify your decision as to whether the regression coefficients for GREQ and GREV (when evaluated separately or after controlling for the other) are statistically significant. Justifying your decision includes providing the parameter(s) being estimated, the statistical test (s) (t, F etc.) and its (their) value, degree(s) of freedom associated with the statistical test(s). (14 p)

i. If someone were to increase their GRE-Quantitative score by 50 points, how much would you expect his or her GPA to change, after controlling for the GRE-Verbal variability? Show how you calculated your answer. (8 p)

j. In your own words explain why you think that the model did not explain all of the variability in GGPA. In other words, what other factors might play a role in increasing the amount of variability explained in GGPA. (8 p)

Answer #1

A researcher compares graduate students’ verbal GRE scores by
their preparatory effort. One group of students did not complete a
GRE preparatory class, one group completed a 3-week GRE preparatory
class, and one group completed a 6-week preparatory class.
Is there a statistically significant difference in average
verbal GRE score among graduate students who did not complete a GRE
preparatory class, completed a 3-week GRE preparatory class, and
completed a 6-week preparatory class?
Given:
No preparatory Class
3-week preparatory Class...

The Graduate Record E (GRE) has a combined verbal and
quantitative mean of 1000 and a standard deviation of 200. Scores
range from 200 to 1600 and are approximately normally
distributed.
a. What percentage of the persons
who take the test score above 1400?
b. What percentage of the persons
who take the test score above 700?
c. Below what score do the bottom
30.9% of the test-takers score?

Amanda took the Graduate Record Examination (GRE), and scored
160 in verbal reasoning and 157 in quantitative reasoning. The mean
score for verbal reasoning was 151 with a standard deviation of 7,
compared with mean µ = 153 and σ = 7.67 for quantitative reasoning.
Assume that both distributions are normal.
(a) What were Amanda’s Z-scores on these exam sections? Mark
these scores on a standard normal distribution curve.
(b) Which section did she do better on, relative to other...

The Graduate Record Examination (GRE) is a standardized test
commonly taken by graduate school applicants in the United States.
The total score is comprised of three compo- nents: Quantitative
Reasoning, Verbal Reasoning, and Analytical Writing. The first two
components are scored from 130 - 170. The mean score for Verbal
Reasoning section for all test takers was 151 with a standard
deviation of 7, and the mean score for the Quantitative Reasoning
was 153 with a standard deviation of 7.67....

1. The Graduate Record Exam (GRE verbal test) has scores that
are normally distributed with a mean of 532 and a standard
deviation of 128. If one test taker is chosen at random, what is
the probability that the person's GRE verbal score is above 500?
Use Table 8.1 and leave answer in decimal form.
2. The Graduate Record Exam (GRE verbal test) has scores that
are normally distributed with a mean of 532 and a standard
deviation of 128....

Quantitative Variable we are interested in comparing: #
of HR’s (Home Run’s)
American
League:
National League:
Sample Size:
28
Sample Size:
22
Sample Mean:
20.14286
Sample Mean:
18.77
Sample Standard
Deviation:
10.44107
Sample Standard
Deviation:
8.257
You are now going to do a two-sample hypothesis test on this
data
Hypothesis: I would expect an American League player to
hit more HR’s (Home Run’s) on average, than a National League
Player?
Introduction: State...

Quantitative Variable we are interested in comparing: #
of HR’s (Home Run’s)
American
League:
National League:
Sample Size:
28
Sample Size:
22
Sample Mean:
20.14286
Sample Mean:
18.77
Sample Standard
Deviation:
10.44107
Sample Standard
Deviation:
8.257
You are now going to do a two-sample hypothesis test on this
data
Hypothesis: I would expect an American League player to
hit more HR’s (Home Run’s) on average, than a National League
Player?
Introduction: State...

1: Sample:
Gender
Verbal
Math
f
630
660
m
610
550
f
680
660
m
490
390
f
510
520
m
700
700
f
640
710
f
520
470
f
530
500
m
640
570
f
710
700
f
630
520
f
670
580
f
630
610
m
360
290
f
540
490
f
490
560
m
730
760
m
760
700
f
530
670
m
710
700
f
630
610
f
530
490
f
420
410
f
490...

The Graduate Management Admission Test (GMAT) is taken by
individuals interested in pursuing graduate management education.
GMAT scores are used as part of the admissions process for more
than 6100 graduate management programs worldwide. The mean sore for
all test?takers is 550 with a standard deviation of 120. A
researcher in the Philippines is concerned about the performance of
undergraduates in the Philippines on the GMAT. She believes that
the mean scores for this year's college seniors in the Philippines...

A graduate student believed that, on the average, college
students spend more time on the Internet compared to the rest of
the population. She conducted a study to determine if her
hypothesis was correct. The student randomly surveyed 25 students
and found that the average amount of time spent on the Internet was
11.75 hours per week with a SD = 1.5 hours. The last census found
that, on the average, people spent 11 hour per week on the
Internet....

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