Exam 1 Practice Test - Stat 212 Exam I Practice 1 A survey...

Stat 212
Exam I
Practice
1. A survey of a random sample of 100 WSU undergraduates revealed that 10
Freshman, 16 Sophomores, 16 Juniors and 18 Seniors owned cell phones. The
total numbers of students in each class were: 20 Freshman, 26 Sophomores, 27
Juniors, and 27 Seniors.
a) Fill in the contingency table below to reflect cell phone ownership
among the undergraduates.
F S J Sr Total
Total 20 26 27 27 100
b) Estimate the probability that a randomly chosen student owns a cell
phone.
60/100 = 0.6
c) Estimate the probability that a randomly chosen student is a freshman.
20/100 = 0.2
d) Estimate the probability that a randomly chosen student owns a cell
phone and is a freshman.
10/100 = 0.1
e) Are the events owning a cell phone and being a freshman independent
events. Justify your answer.
No, because the probability of owning a cell phone and being a
freshman does not equal the probability of owning a cell phone
times the probability of being a freshman. That is,
0.1 ≠ 0.6 x 0.2
f) Given that a student is a senior, estimate the probability that the
student owns a cell phone.
18/27 = 0.667
Cell 60
No Cell 40

2. Use the following output to answer parts a-e below:
a) What is the Slope of the Regression Line?
Slope = 0.00256
b) Is the regression equation very useful? Cite a statistic from the output
to back up your argument.
No, because R-Sq is only 10.4% so only 10.4% of the variation in
GPA is explained by knowing Verbal score meaning that about
90% of the variation is not explained.
c) Is there a positive or negative linear relationship between Verbal and
GPA? Cite evidence from the output above.
Positive because slope is positive (0.00256)
d) Interpret the slope of the regression line.
For each one unit increase in verbal score, there is a 0.00256
increase in GPA.
e) What is the Correlation coefficient?
3. For the Regression Equation: Y = 5 + 2X
a) Find the predicted Y for X=10
Y-hat = 5 + 2 (10) = 25
b) What is the residual for the data point (Y=15, X=6)?
Y-hat = 5 + 2 (6) = 17
Residual = Y – Y-hat = 15 – 17 = -2
The regression equation is
GPA = 1.11 + 0.00256 Verbal
r
2
= 10.4%

4. The Sample Standard Deviation is a “rough” estimate of the average distance
between what?
The average distance between the observations and their mean
5. The Math SAT scores for the seniors at a high school were collected for a study.
An overall mean for all the scores was calculated and the scores were found to fall
into a bell-shaped distribution. One of the seniors, named Bob, had a score of
720.