1 st Semester Exam Review
AP Statistics
The scores of 18 first-year private college women on the Survey of Study Habits and Attitudes are:
154
103
109
126
137
126
115
137
152
165
140
165
154
129
178
200
101
148
The college also administered the test to a sample of 20 first-year men. Their scores were:
108 140 114 91 180 115 126 92 169 146
109 132 75 88 113 151 70 115 187 104
1.
Make a back to back stemplot of the men’s and women’s scores. What is the most noticeable contrast between the two distributions?
Men| |Women
2.
Find the five-number summaries for both distributions.
3.
Are there any outliers according to the 1.5 X IQR criterion?
4.
Make side by side boxplots of the distributions. Use modified boxplots that plot the outliers separately.
5.
I have a special 6-sided die. The numbers 2 and 3 are equally likely to turn up and the numbers:
1, 4, 5, and 6 are twice as likely to turn up as 2 and 3. a.
Create a probability distribution for the die.
X
P(X)
1 2 3 b.
Calculate the expected value and the standard deviation of the die.
4 5 c.
Calculate the probability of rolling a 1, 2, or a 3. d.
Calculate the probability of rolling a prime number.
6

6.
A fair coin is flipped six times. Which outcome, if either, is more likely:
HHHHHT or HTHTTH? Explain briefly.
7.
Suppose that over many years it has been found that on January 16 th in Newport News it rains with a relative frequency of .17, it snows with a relative frequency of .03, and it rains and snows with a relative frequency of .02. What is the probability that on any given January 16 th in the future, it will either rain or snow in Newport News?
UNEMPLOYMENT
A random sample of construction workers was taken in a large city. Of the 150 workers sampled, 16 were
unemployed.
8.
a) Construct and interpret a 90% confidence interval for the proportion of unemployed construction
workers in this city. b) At the time the sample was taken, the overall unemployment rate for the city was 6.8%. Carry out a significance test to determine if there is evidence at the 0.05 significance level to show that the unemployment rate for city construction workers is significantly higher than the overall city rate? Give full statistical analysis to back up your answer.
You are the purchasing agent for a company that must buy a certain type of industrial machine. There are two designs of the machine available, Design A and Design B. You have 200 employees that will be using this machine and could help you decide which machine is better.
9.
Develop and describe a well designed experiment to help you make this decision.
Identify the experimental units, the response variable, how many treatments there are, and describe how you would randomly assign workers to your treatments.

Answers:
1.
Men| |Women Most noticeable difference is that the women’s center of distribution is higher than
5 0 7 the men’s center of distribution.
8 8
2 1 9
9 8 4 10 1 3 9
5 5 4 3 11 5
6 12 6 6 9
2 13 7 7
6 0 14 0 8
1 15 2 4 4
9 16 5 5
17 8
7 0 18
19
20 0
2.
Five number summary for Women: 101, 126, 138.5, 154, 200
Five number summary for Men: 70, 98, 114.5, 143, 187
3.
Women have an outlier of 200.
4.
Women
Men
70 100 130 160 190
SSHA Scores
5.
a.
X
P(X)
1
.2
2
.1
3
.1
4
.2
5
.2
6
.2

b.
 x x

3.7

1.79
c. P(X = 1,2, or 3) = .4 e.
P (X = prime) = .4
6.
These two outcomes are equally likely to occur. There are 2^6 outcomes, all equally likely, and each flip is independent so p =(.5)^6 = 0.15625. Any sequence of 6 outcomes is as likely to occur as any other sequence of 6 outcomes.
7.
P ( rain or snow) = P(rain) + P(snow) – P(rain and snow) = .17 + .03 - .02 = 0.18

8.
Confidence Interval a. The parameter of interest is the true proportion of construction workers in this city that are unemployed. b. Assumptions and conditions:
Independence: Reasonable to believe construction workers are independent of one another
Random condition: The sample of workers was stated as randomly take
10% Condition: 150 should be less than 10% of all construction workers in this large city
Big Enough Sample: np > 10 150

16


150

=16 and nq > 10 150

134


150

=134 >10 c. Assumptions and conditions have been met so I can use an approximately normal model to construct a
90% confidence 1 proportion z-interval for the true proportion of construction workers in this city that are unemployed.
16
150

1.645


16
150


1

16
150
150

90% CI for p: (0.0652, 0.1482)
We can be 90% confident that between 6.52% and 14.82% of the construction workers in this city are unemployed.
Hypothesis Test a. H
0
: The true proportion of construction workers in this city that are unemployed is 6.8%
H p

0
: .068
H a
: The true proportion of the construction workers in this city that are unemployed is greater than
6.8%.
H a
: p

.068
b. The assumptions and conditions have been met previously for the confidence interval. c. z

(.068)(.932)

1.88
is my test statistic
150
P p

.107) d. P-value = (

1.88)

.03
e. With a low P-value of .03 I reject the null hypothesis at the significance level of 0.05. There is statistically significant evidence in favor of the true proportion of construction workers in this city that are unemployed being greater than 6.8%
What do you think might have caused these two decisions to contradict each other?
Ans: roundoff error

9.
The experimental units are the machines
The response variable is the time it takes the workers to complete a task.
There are two treatments: Machine A and Machine B
Answers may vary on the experimental design.
Assign 100 workers randomly to each machine. Do this by assigning each worker a 3 digit number from
001 to 200. Go to the random digits table. Pull three digit numbers ignoring repeats and numbers higher than 200. The first 100 numbers drawn will be assigned to machine A and the rest will be assigned to machine B. Ask each employee to complete the task on the machine and record how long it takes. Average the times for each machine and then compare.