Download sample exam 2

1. Consider the data below of the number of pull-ups six 55 year old men could do before and after a two
week exercise program
before after
6
15
11
18
15
22
9
14
4
10
8
15
a) Make a scatterplot of this data.
b) Describe the relationship: (strength, form, direction).
c) Use your calculator to find the equation of the regression line.
d) Use the data below to verify the equation of the regression line,
a  y  bx
before
after
N
6
6
MEAN
8.83
15.67
MEDIAN
8.50
15.00
before
after
MIN
4.00
10.00
MAX
15.00
22.00
Q1
5.50
13.00
yˆ  a  bx using b  r
sy
sx
,
STDEV
3.87
4.03
Q3
12.00
19.00
Correlation of before and after = 0.944
d) Add the line to your plot. Indicate the coordinates of any points that you computed to plot the line.
e) What is the prediction for someone that can do 10 pull-ups?
f) Find the residual for the point (9,14).
g) What percent of the variation in y is due to a linear relationship?
2. Identify the sampling technique used, and potential sources of problems in each of the examples
below:
a) Students are asked to raise their hands if they will go to the board and present a math problem.
technique
problems
b) Names are drawn from a hat to select students that will go to the board and present a math problem.
technique
problems
c) From a randomly chosen starting place, every 5th name is selected from a list of students in the class
and these students go to the board and present a math problem.
technique
problems
d) Randomly selected homework assignments are used to select students to go to the board.
technique
problems
3. Describe the sample space for the random experiment below:
Choose a student at random. Ask how long it took to commute to school today.
sample space =
4. A recent CNN television show polled the viewers by asking them to log onto the CNN web site and then
post how many minutes per day they use the internet. Explain how this survey technique suffers from bias,
by identifying aspects of the survey that represent:
voluntary response sampling
convenience sampling
undercoverage
nonresponse
5. Use the random number table to select a SRS of size three from a list of 650 people.
6. It is suspected that males and females will react differently to a new form of headache remedy. Outline
a randomized block experiment that could be performed on 20 randomly selected married couples, to
determine if the new remedy is more effective than aspirin. Start at line 105 of the random number table
when you do the randomization to assign treatments to each block. Carefully explain exactly how the table
was used.
7. A recent telephone survey of 200 Pueblo residents found that 146 have visited the new theater
complex.
a) What is the experimental unit?
b) What is the population?
c) What was the sample?
8. Twelve overweight males have agreed to participate in a study of the effectiveness of two weight
reducing regimens: A and B. The researcher first calculates how overweight each subject is by comparing
the subject's actual weight to his ‘ideal’ weight. The subjects and their excess weights in pounds are:
Arthur
Bill
Charlie
Dave
Evan
Frank
12
25
9
43
31
21
George 16
Henry
Issac
Joe
Kevin
Larry
11
33
28
15
24
Diagram and explain how you would perform the experiment, taking into account the fact that subjects that
are more overweight will have an easier time losing weight.
9. Red sports cars tend to be involved in a high percentage of fatal accidents, which leads insurance
companies to believe that cars that are red in color are more dangerous to drive.
a) Explain how this relationship could be due to some other cause.
b) What confounding variable is present in this relationship?
10. Describe the sample space for the random experiment below:
Choose a student at random. Ask if he/she had breakfast today.
sample space =
11. Define the terms
sampling bias
voluntary response sample
confounding
simple random sample
probability sample
stratified random sample
multistage sample
undercoverage
nonresponse
randomized comparative experiment
completely randomized design
statistically significant
block design
matched pairs design
double blind experiment
parameter
statistic
law of large numbers
sampling distribution of a statistic
central limit theorem
Independent events
disjoint events
12. A recent telephone survey of 200 Pueblo residents found that 163 dislike telemarketers. The result
was not surprising, since 88% of people nationwide dislike telemarketers
a) What is the population?
b) What was the sample?
c) Identify any potential sources of bias.
d) Which number is a parameter?
e) Which number is a statistic?
13. To check on the effectiveness of airbags, a consumer group advertised for people with airbags in their
cars to volunteer to participate in an airbag study. The volunteer group was then followed for a year and
their rate of fatal accidents was compared to the overall fatal accident rate. Identify two sources of
confounding in this study. First complete the sentence:
a) Confounding is when . . .
b) Then give variables that could confound the results
14. Consider the probabilities listed below for a randomly chosen USC undergraduate student:
freshman
sophomore
junior senior
.34
.25
.18
??
a) What must be the senior probability?
b) What is the chance a randomly chosen student is not a freshman?
15. Consider the random experiment consisting of tossing three coins: a penny, a dime and a quarter.
a) List the elements of the sample space.
b) The elements of the sample space are equally likely. What would be the probability of getting two
heads?
16. Explain what it means for two events to be disjoint.
17. A certain random number generator randomly produces on of the five listed numbers:
1 , 2 , 3 , 4 , 5. What is the chance it produces an even number, if each number is equally likely?
18. The scores on the ACT college entrance exam in a recent year had a normal distribution with mean
18.5 and standard deviation 6.
a) What is the approximate probability a randomly chosen student scores above 20?
b) Compute the mean and standard deviation of the average score of ten randomly chosen students.
c) What is the approximate probability that the average score of ten randomly chosen students is above
20?
19. Suppose the weights of full grow house-cats vary normally with a mean of 4.3 pounds and a standard
deviation of .8 pounds.
a) What is the probability a randomly chosen cat weighs more than 5 pounds?
b) Compute the mean and standard deviation of the average weight of six randomly chosen cats.
c) What is the probability that this average weight is above 5 pounds?
20. Suppose a given population has mean 27 and standard deviation 5.2.
a) What is the mean and standard deviation of the average of 6 measurements from the population
selected by simple random sampling?
b) What is the probability the average exceeds 28?
21. Your friend is giving a party. He thinks there is a 60% chance Joe will be in attendance, a 40% chance
Mary will show up and a 25% chance they both will attend. \What is the chance neither attends?