AP Stats Review
Assume that the probability that a baseball
player will get a hit in any one at-bat is 0.250.
Give an expression for the probability that his
first hit will next occur on his 5th at bat?
What kind of distribution is this?
A symmetric, mound-shaped distribution has a
mean of 70 and a standard deviation of 10, find
the 16th percentile score.
Girls
90
80
70
75
87
92
86
61
94
100
Boys
70
75
96
92
85
72
63
95
68
98
The table below give the estimated marginal
cost for a piece of furniture. Find the
residual amount for 400 units.
Units
100
200
300
400
500
600
Marginal
Cost
$300
$250
$220
$200
$180
$175
What’s the difference between blocking &
stratifying?
Blocking is used in experiments while
stratifying is used in surveys.
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the
correlation coefficient.
Name each type of sampling method:
A. Code every member of a population and select 100
randomly chosen members.
Simple Random Sample (SRS)
B. Divide a population by gender and select 50 individuals randomly
from each group.
Stratified
C. Select five homerooms at random from all of the homerooms in
a large high school.
Cluster
D. Choose every 10th person who enters the school.
Systematic
E. Choose the first 100 people who enters the school.
Convenience
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Find an estimate of the
population slope if sample is
size 10. (Use 95%)
If I increase the significance level, what
happens to the power of the test? Explain.
If I increase alpha, then Beta decreases. Thus
the power of the test (1-Beta) will Increase.
The specifications fro the length of a part in a
manufacturing process call for a mean of 11.25
cm. Find the probability that a random sample
of 50 of the parts will have a mean of 11.56 cm
or more if the standard deviation is 0.54.
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the coefficient
of determination.
Pre
75
82
45
91
65
75
85
82
78
64
Post
78
81
55
93
65
78
81
86
82
66
A preliminary study has indicated that the
standard deviation of a population is
approximately 7.85 hours. Determine the
smallest sample size needed to be within 2
hours of the population mean with 95%
confidence.
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Find & interpret the slope
Slope = 0.6077
For every addition inch in height, the (yvariable) increases 0.6077 units.
What is the p-value?
It is the probability that I got this sample, as
extreme as it may be, if the Ho was really true.
Explain the power of a test.
It is the probability that rejecting the Ho is
the correct decision. It is found by
calculating 1 – Beta.
A midterm exam in Applied Mathematics consist of
problems in 8 topical area. One of the teachers believe
that the most important of these, and the best
indicator of overall performance, is the section on
problem solving. She analyzes the scores of 36
randomly chosen students using MINITAB, comparing
the total score to the problem-solving subscore.
Give the equation for the least squares regression line.
Predictor
Coef
StDev
T
P
Constant
12.96
6.228
2.08
0.045
ProbSolv
4.0162
0.5393
7.45
0.000
s = 11.09
R-Sq = 62.0%
R-Sq (adj)= 60.9%
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Find the residual amount if the
observed value was (68,37).
She analyzes the scores of 36 randomly chosen students
using MINITAB, comparing the total score to the
problem-solving subscore.
Find and interpret the coefficient of determination.
Predictor
Coef
StDev
T
P
Constant
12.96
6.228
2.08
0.045
ProbSolv
4.0162
0.5393
7.45
0.000
s = 11.09
R-Sq = 62.0%
R-Sq (adj)= 60.9%
She analyzes the scores of 36 randomly chosen students using
MINITAB, comparing the total score to the problem-solving
subscore.
Find and interpret the slope.
Predictor
Coef
StDev
T
P
Constant
12.96
6.228
2.08
0.045
ProbSolv
4.0162
0.5393
7.45
0.000
s = 11.09
R-Sq = 62.0%
R-Sq (adj)= 60.9%
She analyzes the scores of 36 randomly chosen students
using MINITAB, comparing the total score to the
problem-solving subscore.
Find an estimate for the slope. Justify your answer.
Predictor
Coef
StDev
T
P
Constant
12.96
6.228
2.08
0.045
ProbSolv
4.0162
0.5393
7.45
0.000
s = 11.09
R-Sq = 62.0%
R-Sq (adj)= 60.9%
She analyzes the scores of 36 randomly chosen students using
MINITAB, comparing the total score to the problem-solving
subscore.
Can you justify that there is a linear relationship – using
statistical justification? Show it!
Predictor
Coef
StDev
T
P
Constant
12.96
6.228
2.08
0.045
ProbSolv
4.0162
0.5393
7.45
0.000
s = 11.09
R-Sq = 62.0%
R-Sq (adj)= 60.9%
Reject Ho since pval < alpha (0.05).
There is a linear relationship between
Problem Solving subscore and test score.
The table below specifies favorite ice cream flavors by
gender. Is there a relationship between favorite flavor
and gender?
Male
Female
Chocolate
32
16
Vanilla
14
4
Strawberry
3
10
A study of 20 teachers in a school district indicated that the
95% confidence interval for the mean salary of all teachers in
that school district is ($38,945, $41, 245).
What assumptions must be true for this confidence interval to
be valid?
A. No assumptions are necessary. The Central Limit Theorem
applies.
B. The sample is randomly selected from a population of
salaries that is a t-distribution.
C. The distribution of the sample means is approximately
normal.
D. The distribution of teachers’ salaries in the school district
is approximately normal.
E. The standard deviation of the distribution of teachers’
salaries in the school district is known.
Predictor
Constant
height
Coef
-4.792
0.6077
SE Coef
T
8.521
-0.56
0.1236
4.92
P
0.594
0.003
S = 0.932325 R-Sq = 80.1% R-Sq(adj) = 76.8%
Can you prove that a linear
relationship exists? Show it!
Reject Ho since pval < alpha (0.05).
There is a linear relationship between
height and (y variable).
A study of 20 teachers in a school district indicated that the
95% confidence interval for the mean salary of all teachers in
that school district is ($38,945, $41, 245).
Explain what is meant by the 95% confidence interval.
We are 95% confident that the mean salary of all teachers
in the school district is between $38,945 and $41,245.
Explain what is meant by the 95% confidence level.
If we repeat this process over and over, 95% of the
intervals formed will contain the true population mean.
If an NFL quarterback’s pass completion
percent is 79%, what is the probability that he
will only complete 15 of 30 passes in his next
game?
If an NFL quarterback’s pass completion
percent is 79%, what is the probability that he
will only complete 15 of 30 passes in his next
game?
Give me two other ways of stating the formula
for the previous problem.
If an NFL quarterback’s pass completion
percent is 79%, what is the probability that he
will only complete 15 of 30 passes in his next
game?
Does this problem really meet the criteria for a
binomial variable?
Yes – It is binomial – 2 possibilities (complete or don’t complete)
Independent
n is fixed
success probability does not change
A candy make coats her candy with one of three colors: red, yellow,
or blue, in published proportions of 0.3, 0.3, and 0.4 respectively. A
simple random sample of 50 pieces of candy contained 8 red, 20
yellow, and 22 blue pieces. Is the distribution of colors consistent
with the published proportions. Give appropriate statistical
evidence to justify your answer.
Obs
8
20
22
Exp
15
15
20
X^2
3.2667
1.6667
0.2
5.13
P1=prop red
P2=prop yellow
P3=prop blue
All cells >5
Chi Sq Goodness of Fit
The primary air exchange system on a proposed
spacecraft has four separate components (A, B,
C, D) that all must work properly for the system
to operate well. Assume that the probability of
any one component working is independent of the
other components. It has been shown that the
probabilities of each component working are P(A)
= 0.95, P(B) = 0.90, P(C )= 0.99, and P(D) = 0.90.
Find the probability that the entire system
works properly.
The primary air exchange system on a proposed
spacecraft has four separate components (A, B,
C, D) that all must work properly for the system
to operate well. Assume that the probability of
any one component working is independent of the
other components. It has been shown that the
probabilities of each component working are P(A)
= 0.95, P(B) = 0.90, P(C )= 0.99, and P(D) = 0.90.
What is the probability that at least one of the
four components will work properly?
The only time you don’t have at least one is when
you have none.
P(at least 1) =
=
=
=
1 – P(none)
1 – [0.05 * 0.1 * 0.01 * 0.1]
1 – 0.00005
0.999995