AP Stats Review

1
AP Stats Review
2
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?
 
3
A symmetric, mound-shaped distribution has a mean
of 70 and a standard deviation of 10, find the
16th percentile score.
 
4
 
Girls 90 80 70 75 87 92 86 61 94 100
Boys 70 75 96 92 85 72 63 95 68 98
5
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
 
6
Whats the difference between blocking
stratifying?
Blocking is used in experiments while stratifying
is used in surveys.
7
Find interpret the correlation coefficient.
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
 
8
 
9
Name each type of sampling methodA. 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. StratifiedC. Select five homerooms at
random from all of the homerooms in a large high
school. ClusterD. Choose every 10th person
who enters the school. SystematicE. Choose
the first 100 people who enters the
school. Convenience
10
Find an estimate of the population slope if
sample is size 10. (Use 95)
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
 
11
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.
12
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.
 
13
Find interpret the coefficient of determination.
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
 
14
 
Pre 75 82 45 91 65 75 85 82 78 64
Post 78 81 55 93 65 78 81 86 82 66
15
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.
 
16
Find interpret the slope
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
Slope 0.6077 For every addition inch in
height, the (y-variable) increases 0.6077 units.
17
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.
18
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.
19
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 62.0 R-Sq (adj) 60.9 R-Sq (adj) 60.9
 
20
Find the residual amount if the observed value
was (68,37).
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
 
21
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 62.0 R-Sq (adj) 60.9 R-Sq (adj) 60.9
 
22
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 62.0 R-Sq (adj) 60.9 R-Sq (adj) 60.9
 
23
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 62.0 R-Sq (adj) 60.9 R-Sq (adj) 60.9
 
24
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 62.0 R-Sq (adj) 60.9 R-Sq (adj) 60.9
 
 
Reject Ho since pval lt alpha (0.05). There is a
linear relationship between Problem Solving
subscore and test score.
25
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
 
26
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.
 
27
Can you prove that a linear relationship exists?
Show it!
Predictor Coef SE Coef T
P Constant -4.792 8.521 -0.56
0.594 height 0.6077 0.1236 4.92
0.003 S 0.932325 R-Sq 80.1
R-Sq(adj) 76.8
 
 
Reject Ho since pval lt alpha (0.05). There is a
linear relationship between height and (y
variable).
28
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.Expl
ain what is meant by the 95 confidence
level.
We are 95 confident that the mean salary of all
teachers in the school district is between
38,945 and 41,245.
If we repeat this process over and over, 95 of
the intervals formed will contain the true
population mean.
29
If an NFL quarterbacks pass completion percent
is 79, what is the probability that he will only
complete 15 of 30 passes in his next game?
 
30
If an NFL quarterbacks 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.
 
31
If an NFL quarterbacks 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 dont complete) Independent n
is fixed success probability does not
change
32
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 Exp X2
8 15 3.2667
20 15 1.6667
22 20 0.2

5.13
P1prop red P2prop yellow P3prop blue All
cells gt5 Chi Sq Goodness of Fit
 
33
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.
 
34
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 dont 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