Question
In: Statistics and Probability
14. For a sample of students, their total SAT scores and college grade point averages (GPA)...
14. For a sample of students, their total SAT scores and college grade point averages (GPA) are given below.
SAT GPA
1070 3.50
1040 2.66
1120 3.54
1260 3.83
1100 2.60
1020 2.70
960 2.00
a. Make a scatterplot on your calculator. Does there appear to be a linear relationship between SAT scores and GPA?
b. Find the least squares regression line. Round all constants to 4 decimal places.
c. Use your equation to predict the college GPA of a student with a 1000 SAT score.
d. Find the correlation coefficient, rounded to 3 decimal places. What does this tell you about the relationship between the two variables?
Solutions
orchestra answered 1 year agoRelated Solutions
The grade point averages (GPA) for 12 randomly selected college students are shown on the right....
The grade point averages (GPA) for 12 randomly selected college
students are shown on the right. Complete parts (a) through (c)
below. Assume the population is normally distributed.
2.2 3.4 2.9 1.8 0.8 4.0 2.4 1.3 3.9 0.5 2.4 3.3
(a) Find the sample mean.
x = _____ (Round to two decimal places as needed.)
(b) Find the sample standard deviation.
s= ______ (Round to two decimal places as needed.)
(c) Construct a 95% confidence interval for the...
The grade point averages (GPA) of 18 randomly selected college students are used to estimate the...
The grade point averages (GPA) of 18 randomly selected college
students are used to estimate the mean GPA of the college students.
The GPAs from the sample are as follows:
2.3 3.3 2.6 1.8
0.2
3.1 4.0 0.7
3.1
2.3 2.0 3.1 3.4 1.3 2.6 2.6
3.7 2.2
(5 points) Is it justified to use of the standard normal
distribution to construct the confidence interval? Explain.
(10 points) If the population is assumed to be normally
distributed, construct a 98% confidence interval for the population
mean GPA. Show your work in...
1. The grade point average (GPA) of a large population of college students follows a normal...
1. The grade point average (GPA) of a large population of
college students follows a normal distribution with mean 2.6, and
standard deviation of 0.5. Students with GPA higher than 3.5 are
considered “exceptional”, 3.0 to 3.5 are considered to be “good”,
2.0 to 3.0 are considered “average”, and below 2.0 are considered
to be “poor”.
(a) For a randomly selected student, what is the probability
that he has a “good” GPA?
(b) Suppose 10 students are randomly selected. Let...
QUESTION 3 The following table contains ACT scores and the GPA for eight college students. Grade...
QUESTION 3
The following table contains ACT scores and the GPA for eight
college students. Grade point average is based on a four-point
scale and has been rounded to one digit after the decimal.
Student
GPA
ACT
1
2.8
21
2
3.4
24
3
3
26
4
3.5
27
5
3.6
29
6
3
25
7
2.7
25
8
3.7
30
You estimate the following relationship between GPA and ACT:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.759884064
R Square
0.577423791...
The grade point averages (GPAs) of a large population of college students are approximately normally distributed...
The grade point averages (GPAs) of a large population of college
students are approximately normally distributed with mean 2.5 and
standard deviation 0.7. If students possessing a GPA less than 1.75
are dropped from college, what percentage of the students will be
dropped? (Round your answer to two decimal places.)
?? %
The width of bolts of fabric is normally distributed with mean
950 mm (millimeters) and standard deviation 10 mm.
(a) What is the probability that a randomly chosen...
Sample grade point averages for ten male students and ten female students are listed. Find the...
Sample grade point averages for ten male students and ten female
students are listed. Find the coefficient of variation for each of
the two data sets. Then compare the results. Males 2.6 3.8 3.9 3.8
2.7 2.6 3.4 3.5 3.8 1.8 Females 2.7 3.9 2.2 3.8 3.5 4.1 2.1 3.8 3.9
2.5 The coefficient of variation for males is nothing%. (Round to
one decimal place as needed.)
Sample grade point averages for ten male students and ten female students are listed. Find the...
Sample grade point averages for ten male students and ten female
students are listed. Find the coefficient of variation for each of
the two data sets. Then compare the results
Males 2.5 3.8 3.6 3.9 2.6 2.6 3.6 3.2 3.9 1.8
Females 2.8 3.5 2.1 3.7 3.5 4.1 2.1 3.9 3.9 2.3
The coefficient of variation for males is __%.
The Coefficient of variation for females Is __ %
To estimate the average SAT scores of students in a college, six students in the college...
To estimate the average SAT scores of students in a college, six
students in the college are randomly selected and their SAT scores
are as follows: 1350, 1450, 1320, 1480, 1300, 1400.
(a) (3 points) What is the population of interest?
(b) (3 points) What is the value of sample median?
(c) (6 points) What is the lower quartile Q1 and the upper
quartile Q3 ?
(d) (3 points) What is the value of sample mean?
(e) (5 points) What...
SAT reading and writing section scores of a random sample of twenty 11th-grade students in a...
SAT reading and writing section scores of a random sample of
twenty 11th-grade students in a certain high school are given
below.
380 520 480 510 560 630 670 490 500 550
400 350 440 490 620 660 700 730 740 560
Test if the standard deviation of the reading and writing section
SAT score of the students in this school is higher than 100. What
is the value of the test statistic (round off to the nearest
integer)?
The data below provides College GPA, High School GPA, SAT total score, and a number of...
The data below provides College GPA, High School GPA, SAT total
score, and a number of letters of reference. a.Generate a model for
college GPA as a function of the other three variables? b.Is this
model useful? Justify your conclusion. c.Are any of the variables
not useful predictors? Why? CGPA HSGPA SAT REF 2.04 2.01 1070 5
2.56 3.4 1254 6 3.75 3.68 1466 6 1.1 1.54 706 4 3 3.32 1160 5 0.05
0.33 756 3 1.38 0.36 1058...
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