Download Mathematics 243, Lewis - Linn

Mathematics 243, Rob Lewis
Final Exam Practice Problems
Part I
Fill in the blank.
1. A college counselor observes people waiting for the bus and records whether they are
sitting alone or not.
Identify: a) the individual
b) the variable
c) type of variable
________________ _______________
__________________
2. Students are given a tennis ball and asked to throw it as far as possible. The distance
it goes is recorded.
Identify: a) the individual
b) the variable
c) type of variable
________________
_______________
__________________
3. If a distribution is skewed to the right what can you say about the mean and median?
4. An extreme outlier is added to the data what statistical measurement changes most?
5. What is the standard deviation of a standard normal distribution:
6. On a particular statistics final exam, the maximum number of points a student could
earn was 200. Here is a sample of student test scores from the class:
121, 142, 118, 179, 146, 133, 124, 128, 137, 116
a. Use a ruler to draw an accurate boxplot of the data. Label each component and
its numerical value. For example, label the location of Q3 and its value.
b. Use the Interquartile Range to test for outliers. Are there any? Explain briefly.
7. Six students were asked how many classes they missed in all their courses last term.
The results are shown in a list below. Calculate the mean and record below the data.
Demonstrate how to calculate the standard deviation “by hand” , i.e using the
formula.
X
12
11
8
12
5
6
x ______
s ______
8. On the normal distribution provided, label the
mean, plus/minus 1 standard deviation,
plus/minus 2 standard deviations, and plus/minus
3 standard deviations.
For the next three problems use the following
information. Suppose the Print-Rite Company is
interested in the number of continuous hours their
printers will operate before mechanical failure. Previous sampling has shown that the
data follows a normal distribution (bell curve shape histogram) with a mean of 280 hours
and a standard deviation of 18 hours.
9. What percent of the printers will last between 250 and
270 hours? Shade in the appropriate area.
10. Suppose the number of hours the printer last before
failure is N(300, 22). Calculate: P( X < 340). Shade in
the appropriate area.
11. Provide a reasonable five-number summary of the
length of time the
Measurement
Value
printers will last
assuming the
mean is 280
hours with standard deviation 18 hours. You are
not required to use the normal graph below.
12. My son, Jimmy, is practicing his target
shooting with a sling shot. Out of 30 attempts
he hit his target 9 times. Before his next shot
he tells me that he as 0.30 probability of
hitting the target with his next shot. This is
an example of what type of probability?
13. I watch my son hit the target 9 times out of
30. I think he has a higher probability of 0.40
of hitting the target. This is an example of
what type of probability?
14. Jordon is interested in how long it takes people to find a parking spot at
LBCC between 8 am and 2 pm. He randomly samples 5 cars every hour
starting at 8 am and records the driver’s gender and how long they take to
park. What type of study is this?
Voluntary Experiment Survey Observational None of the above
15. Jordon is interested in how long it takes people to find a parking spot at
LBCC between 8 am and 2 pm. Starting at 8 am he selects every fifth car
entering the parking lot. What type of sampling is he using?
Convenience Voluntary SRS Systematic Cluster Stratified
16. Jordon is interested in how long it takes people to find a parking spot at
LBCC between 8 am and 2 pm. He randomly samples 5 cars every hour
starting at 8 am. What type of sampling is he using?
a. Convenience
b. Voluntary
c. SRS
d. Systematic
e. Cluster
f. Stratified
17. Jordon is interested in how long it takes people to find a parking spot at
LBCC between 8 am and 2 pm. He places a survey form on each car
window asking the driver to record the amount of time it takes them to park
the next day and to return the form to a collection box in Takena Hall. What
type of sampling is this?
a. Convenience
b. Voluntary
c. SRS
d. Systematic
e. Cluster
f. Stratified
18. A probability model with a finite sample space is a __________________
probability model. A probability model which assigns probabilities as the
area under a density curve is a __________________ probability model.
19. (8 pts) The United States Census of all citizens reported the average number
of children under age 18 per household is 2.4 with standard deviation 0.8. A
study consisting of a random sample of 50 Oregonians reported the average
number of children is 2.1 with standard deviation 1.2.
Identify whether the value is a parameter or statistic, and its symbol.
Value
50
2.1
0.8
2.4
Parameter or Statistic
Symbol
20.
An industrial psychologist is interested in studying the effect of room
temperature and humidity on the performance of tasks requiring manual
dexterity. She chooses three temperatures of 65 degrees Fahrenheit, 80
degrees Fahrenheit and 95 degrees Fahrenheit with humidity of 60% and
80%. She plans to measure the number of correct insertions, during a 15minute period using a peg-and-hole apparatus requiring the use of both
hands simultaneously. After each subject is trained on the apparatus, he or
she is asked to make as many insertions as possible in a 15-minute period.
Sixty factory workers from each of three different companies are to be
randomly assigned to the different temperature and humidity combinations.
(16 pts)
a.
b.
c.
d.
e.
f.
Identify the population under study.
Identify the “individuals” units in this experiment.
What are the factors?
How many treatments are there? Specify two of these treatments.
What blocking variable(s) are reasonable? Why?
What is the response variable?
21. (24 pts) Assume the weights of oranges at the grocery store follow
approximately a normal distribution with mean 7.5 oz and standard deviation
2.1 oz.
a. What is the probability of selecting 9 oranges with a mean weight
between 7.5 oz and 8.5 oz? Show your work using the proper notation.
Shade in the area under the
normal curve correctly.
b. What is the probability of
selecting 9 oranges with a mean
weight less than 6.5 oz? Show
your work using the proper
notation. Shade in the area
under the normal curve
correctly.
c. What is the probability of a
single randomly selected
orange having a weight
between 7.5 oz and 8.5 oz ?
Show your work using the
proper notation. Shade in the
area under the normal curve
correctly.
d. Complete this statement: “The
probability of a random sample of
25 oranges falling between _______ and _______ is 0.95. “ Show your
work.
Part II.
1. Three stellar stats researchers independently select random samples from the same
population. The sample sizes are 1000 for Sarah, 4000 for Lewis, and 250 for TJ.
Each researcher constructs a 95% confidence interval. Match the following
margins of error with the correct researcher: 0.015
0.031
.062
2. Julie selects 100 subjects at random from a population, observes 50 successes, and
calculates three confidence intervals. The confidence levels are 90%, 95%, and
99%. Match the each confidence interval below with the confidence level:
(.402,.598)
(.371,.629)
(.418,.582)
3. Explain:Teagan reports in her study about the effect of new drug to improve
recovery rates of stroke victims a p-value of 0.0351. She decides to “reject the
null hypothesis”. James says no way. Who is right? Explain.
4. Vanessa reports in her study a p-value of 0.042 and a confidence interval for the
difference between the average reaction time of men and women. Circle the
confidence interval(s) below that would have been possible in her study.
95% Confidence Interval: (-2.2, 10.2)
95% Confidence Interval: (1.1, 13.1)
99% Confidence Interval: (-3.2, 12.6)
99% Confidence Interval: (0.4, 15.8)
5. Child psychologist, Dr. Porter reports that children ages 2-3 will spend on average
3.4 hours per day by themselves in a day care environment. Her mean was based
on a sample of 49 children and had a standard deviation of 4.8 hours. She reported
a confidence interval of (2.3 , 4.5).
a) What was the standard error of the mean? ____________________
b) What was the margin of error? _____________________________
c) What was the confidence level? ____________________________
d) What was the value of ? _________________________________
e) Name two actions she could take to decrease the margin of error.
6. Health advocate Wes volunteers his time to test homes in her hometown for
excessive lead dust. Lead dust is known to cause learning disabilities in children
and is found in older homes where lead paint has been used. In a random survey
of the area he found that 300 homes out of 450 had excessive levels of lead dust.
a)
b)
c)
d)
e)
f)
g)
What is the experimental unit? ___________
What is the variable? _________________________
What is the symbol of the parameter being estimated? _____________________
What does this parameter represent in the context of this problem?
What is the symbol for the sample statistic? ______________________________
What is the value of the sample statistic? ________________________________
Report your results using a 99% complete confidence interval statement.
7. ODOT engineers Sawyers and Salinas did a small pilot study of the Highway 99
and Oakville Road intersection. They wrote down the following times in seconds
between when a car turns onto Oakville Road and a car on Highway arrives at the
intersection:
0.6
1.3
2.8
.4
.8
5.1
1.2
1.1
5.4
.5
1.0
3.2
a)
b)
c)
d)
e)
f)
g)
What is the experimental unit? ___________
What is the variable under study? _________________________
What is the symbol of the parameter being estimated? ________________
What does this parameter represent in the context of this problem?
What is the symbol for the sample statistic? ______________
What is the value of the sample statistic? _______________
Report your results using a complete 95% confidence interval statement.
8. The new director of the LBCC nursing school, Dr. W, is concerned with the
percentage of students who successfully complete the nursing program. He
wonders how the 66% success rate at LBCC compares with other schools in the
region. He hires statistical consultant, Dr. Mu, to randomly survey 1200 entering
students from nursing schools across Oregon, Washington, and California. Dr. Mu
reports that only 550 of these students successfully complete their nursing
program.
In Words
Mathematically
Ho:___________________________________________ Ho: ___________
___________________________________________
HA:___________________________________________
___________________________________________
HA: ___________
9. Senator Margie O’Error was elected based largely on her efforts to increase
funding for mathematics education in the United States. As a result of smaller
classroom size and better-trained teachers, she believes that American children
now might be performing at a higher level in mathematics than European children
of the same age.
In Words
Mathematically
Ho:___________________________________________ Ho: ___________
HA:___________________________________________
HA: ___________
10. Ms. Creel is concerned about her 4000 employees taking excessive amounts of
sick leave. She reads in a business journal that the nationwide average number of
sick days per person is 4.58 days per year. She analyzes a random sample of 20
employee records. She records a sample mean of 8.12 days per year and a sample
standard deviation of 8.34 days per year.
In Words
Ho:___________________________________________
Mathematically
Ho: ___________
HA:___________________________________________
HA: ___________
11. Safety racing engineer Dr. Lee Sigma designs a device which projects a red color
on your windshield in front of you when your car is approaching another car too
quickly, i.e. you need to brake! He hopes that the extra visual aide will reduce the
amount of time it takes for the car to stop. He records the stopping distances of 35
drivers using a normal car. He then measures the stopping distance, at the same
speed, for the same 35 drivers driving the same car outfitted with the visual aide
device.
In Words
Mathematically
Ho:___________________________________________ Ho: ___________
HA:___________________________________________
HA: ___________
12. Analyze question #8 and #10
a) What is your “decision” based on your p-value?
b) What conclusion would you draw?
13. Based on a random sample of four hundred fifty tacks we are _____% confident
that the true proportion of tacks that will land face up when dropped from a height
of five feet is between .26 and .34.
a. What is p̂ ?
b. What is the margin of error?
c. What confidence level was used? (No guesses, show your work!)