Download exp obs - Mister Youn

AP Statistics
Review Chapters 26 – 27)
MULTIPLE CHOICE
Name: __________________________________________ Per: ____
Write the letter corresponding to the best answer in the blank provided.
In a study of the performance of a computer printer, the size (in kilobytes) and the printing time (in seconds) for
each of 22 small text files were recorded. A regression line was a satisfactory description of the relationship
between size and printing time. The results of the regression analysis are shown below.
___1.
Variable
Size
Constant
Coefficient
3.47812
11.6559
s = 0.6174
R-squared = 87.5%
B) 11.6559
C) 0.3153
D) 11.6559  2.086  0.3153
E) 11.6559  1.725  0.3153
B) 0.9354/60
C) 0.9354 + 20
D) 0.9354
E) more information is needed
What is the proportion of observed variation in printing time that can be explained by the linear
relationship of size and printing time?
B) 0.875
C) 0.3153
D) 0.0001
E) none of these
Which of the following does a small value of 2 indicate?
A)
B)
C)
D)
E)
___ 6.
E) 0.875
The correlation between file size (in kilobytes) and printing time (in seconds) for this regression analysis is
0.9354. If we convert the printing times from seconds to minutes (divide by 60) and add 20 kilobytes to each
file size, what will be the value of the correlation?
A) 0.294
___ 5.
D) 3.47812
Which of the following should be used to compute a 95 percent confidence interval for the slope of the
regression line?
A) (0.9354/60) + 20
___ 4.
probability
<0.0001
<0.0001
R-squared (adjusted) = 86.9%
A) 3.47812  2.086  0.294
B) 3.47812  1.96  0.6174
C) 3.47812  1.725  0.294
___ 3.
t-ratio
11.8
37
What is the average change in printing time for every increase of one kilobyte in size of the printer?
A) 0.294
___2.
s.e. of Coeff
0.294
0.3153
The observed cell counts are reasonably similar to the expected counts.
The differences between the observed and expected cell counts are significantly large.
A small probability of observing a statistic at least as large as the one observed given that Ho is true.
The probability of correctly rejecting a false null hypothesis
None of the above
The test statistic 
(obs  exp) 2
has a distribution that is
exp
A) normal
B) uniform
C) left-skewed
D) bimodal
E) right-skewed
7.
A biology professor at PU (good ol’ Podunk!) teaches several very large sections of introductory biology (note:
her graduate student assistants teach the lab sections). Historically, her grades have been distributed as
follows: 15% As 30% Bs 40% Cs 10% Ds
5% Fs
A random sample of her grades from last semester has the following distribution:
Grade
A
B
C
D
F
Total
Proportion of historical grades
0.15
0.30
0.40
0.10
0.05
1.00
Number of observed grades
68
91
58
19
8
244
Test an appropriate hypothesis to decide if the professor’s most recent grade distribution matches the historical
distribution. Give statistical evidence to support your conclusion. (hint: in order to do this problem, you should start by
calculating the expected number of grades in each letter category)
8.
A random sample of 200 students was selected from a large college in the United States. Each selected student
was asked to give his or her opinion about the following statement.
"The most important quality of a person who aspires to be the President
of the United States is a knowledge of foreign affairs."
Each response was recorded in one of five categories. The gender of each selected student was noted. The data
are summarized in the table below:
Strongly
Disagree
Male
10
Female
20
Response Category
Neither
Somewhat
Somewhat
Agree nor
Disagree
Agree
Disagree
15
15
25
25
25
25
Strongly
Agree
25
15
Is there sufficient evidence to indicate that the response is dependent on gender? Provide statistical evidence
to support your conclusion.
9.
A certain brand of bite-sized candies comes in three varieties: smooth, crunchy, and chewy. The manufacturer
is interested if preferences for the types of candies differ between three school-age groups: elementary, middle,
and high school. Separate random samples of students at the three local schools, one of each age group, are
taken, and the data from the samples is compiled in the table below.
Variety of Candy
Population
Elementary
Middle
High School
Creamy
33
21
16
Crispy
14
16
12
Chewy
19
17
32
a) At the 1% level of significance, is there evidence that the proportion of students that prefer each variety of
candy differs among the various age groups?
b) Based on your conclusion in part (a), which type of error (Type I or Type II) might the candy manufacturer
have made? Describe this error in the context of the scenario.
10.
A random sample of 11 high school students produced the following results for number of hours of television
watched per week and GPA.
High school students
Scatter Plot
3.8
Scatter Plot
2.6
2.0
5
10
15
20
TV_Hours
Coef
3.8
-0.0558
StdDev
2.0426
0.01769
Histogram
1
2.6
25
High school students
3
2
0.4
0.0
-0.4
-0.8
3.2
Predictor
Constant
Hours
High school students
3.0
3.4
pred_GPA
T
1.86
-3.154
3.8
P
0.05
0.012
-0.8
-0.4 0.0 0.4
residuals
0.8
s = 0.355
R-sq = 53%
a) State the least squares regression equation in context.
b) State and interpret the slope in context.
c) Are the conditions for inference met?
d) Is there evidence of a relationship between the number of hours of TV a high schooler watches and
his/her GPA? Test an appropriate hypothesis and state your conclusion in proper context. At this point,
assume that all conditions for inference have been met.
e) Construct a 95% confidence interval to estimate the slope of the least squares regression line.