True or False: A parameter is a numerical summary of a variable for a sample.
Unit 1 Practice problems: False. A parameter is a numerical summary of a variable for a population. A
statistic is a numerical summary of a variable for a sample.
A local radio station is interested in determining how North Carolina residents feel about
marijuana legalization. The station set up a special phone number which could be called
by people who wished to voice their opinion. The station found that 67% of t
Unit 1 Practice problems i) The proportion of all North Carolina residents who support marijuana legalization.
ii) All North Carolina residents
iii) 67%, the proportion of callers who support the legalization of marijuana.
iv) The 1,624 people who called
True or False: Non-response bias occurs when a subset of the sample cannot be contacted
or does not respond.
Unit 1 Practice Problems True
True or False: Cluster sampling involves dividing the sampling frame into groups, and then
randomly sampling within each group.
Unit 1 Practice problems False. This is stratified! Cluster sampling randomly selects the entire groups.
The amount of data used by mobile customers has skyrocketed in recent years. Of great
concern is how to provide fast and reliable data service at a reasonable cost to customers.
Some mobile service companies (like AT&T) are considering charging app provid
Unit 1 practice Problems
i) App developers who provide apps to the iPhone app store.
ii) The proportion of developers who provide apps to the iPhone app store that are willing
to pay for data usage.
iii) Response bias because of the question wording (subs
The Chief Financial Officer (CFO) at a national retailer would like to estimate the average
amount spent by all Americans on Valentine's Day. He surveys 5,819 people on the company's
catalog mailing list, asking them to report the amount they spent on gif
Unit 1 Practice Problems i) All Americans.
ii) The 5,819 people on the company's mailing list that were surveyed.
iii) The average amount spent by all Americans on gifts, food, and entertainment for
Valentine's Day
iv) $130.97, which is the average amount
Which of the following is true about a parameter?
a) It is typically known
b) Its a numerical summary of the population
c) Its a numerical summary of the sample
d) Both a and b
Unit 1 Practice Problems
b) It's a numerical summary of the population
A campaign for a local politician wants to estimate the proportion of voters in a large
urban county that plan to vote in an upcoming election. To do so, they take a sample of
150 people who "liked" the candidate on Facebook.
i) What is the population of
Unit 1 practice problems
i) Voters in a large urban county
ii) The 150 people they selected who like the candidate on Facebook
iii) The proportion of voters in a large urban county that plan to vote in an upcoming
election
iv) No, the sample is not repres
An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made the exam harder than he had intended. The scores were very symmetric, but the average score for his students was 61 and the stan
Method 1 will increase the standard deviation of the students' scores (Q2)
A college professor stops at McDonald's every morning for 10 days to get a number 1 value meal costing $5.39. On the 11th day he orders a number 8 value meal costing $4.38.
Which of the following are true?
Select all that apply.
Select one or more:
During
During the first 10 days, the professor's standard deviation was 0. (Q2)
After taking an aptitude test, the computer told Bob that he had a z-score of 1.08.
If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score?
Select all that apply.
Select one or more:
Bob
Bob scored within 2 standard deviations of the mean score. Bob did better than the mean score. About 14% of students taking the aptitude test did better than Bob. (q2)
The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard dev
0.8944 (Q2)
For a normal distribution, what standard score (Z-score) has 10% of the distribution above it? Find the closest value listed on the table. 2 decimal places
1.28 (Q2)
Which of the following are NOT likely to be well modeled by a normal distribution because the distribution is NOT likely to be symmetric? (Hint: Sketch what you think the histogram would look like based on the information given.)
Select one or more:
a. Th
A, B, D (Q2)
A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 531 and a standard deviation of 66. A local Junior High principal has decided to
615 (Q2)
A researcher believes that the ankle circumference for adult females in Europe can be considered to have a normal distribution with a mean of 20 cm.If his belief is correct which of the following ranges of ankle sizes will have the largest proportion of m
17 to 23 (Q2)
a) Vanessa scored 83 on her History final. The class average was 74, and the standard
deviation was 8 points. What is Vanessa's standardized score?
b) Marcus is also in Vanessa's class. His standardized score was 1.75. How many points
did he score on the
Unit 2 Practice Problems
a)
y ? �
?
=
83 ? 74
8
= 1.125
b) Marcus scored 1.75 standard deviations above the mean ? �+1.75�? = 74+1.75�8 = 88.
You can show this is true using algebra.
c) Below, his normal score is negative, so he scored less than the mean.
A company that markets build-it-yourself furniture sells a computer desk that is advertised
with the claim "less than an hour to assemble." However, through post purchase surveys
the company has learned that only 25% of its customers succeeded in building
Unit 2 practice Problems We want to rewrite our claim so that way 60% of our customers have finished assembling
the desk. By changing our percentage from 25% to 60%, our new standard score is z = .25.
What we want to do with this problem is identify a new
Would you expect distributions of these variables to be uniform, unimodal, or bimodal?
Symmetric or skewed? Explain why.
a) Ages of people at a Little League game.
b) Number of siblings of people in your class.
c) Pulse rates of college-age males.
d) Numb
Unit 2 Practice Problems
a) Bimodial because you have players and parents. It may also be skewed to the right,
since parents' ages can be higher than the mean more easily than lower.
b) Unimodal and skewed to the right. There are probably many students wi
A meteorologist preparing a talk about global warming compiled a list of weekly low temperatures
(in degrees Fahrenheit) he observed at his southern Florida home last year. The
coldest temperature for any week was 36? F, but he inadvertently recorded the
Unit 2 Practice Problems
a) The mean will be smaller; the median will not be affected.
b) The range and standard deviation will be larger; the IQR won't change
A large organization with membership consisting of professionals with or without an M.D.
degree wanted to know the average income of its members. Name the type of sampling
plan they used in each of the following scenarios:
a) They numbered all the members
Unit 2 practice Problems
a) They numbered all the members using an alphabetical list and generated 1000 random
numbers. Members corresponding to the numbers are selected for the sample.
b) They randomly selected 500 members from a list of all professional
In a Midwestern state an automobile insurance company has a large number of customers. From company files it is known that 86% of the customers have only the state minimums for insurance. An official with the state board of insurance is going to take a ra
.0347 (q3)
In a sample of 100 students, what is the probability that over 35% of the sample has AP credit?
Give your answer to 4 decimal places
.1379 (q3)
In a sample of 200 students, what is the probability that over 33% of the sample has AP credit?
Give your answer to 4 decimal places
.1762 (q3)
According to a recent report it was found that 48.7% of residents in Franklin county Ohio are registered to vote. Which of the following is more likely.
Select one:
We take a random sample of 30 people from this county and find that the proportion is less
We take a random sample of 30 people from this county and find that the proportion is less than 45%. (q3)
At a large university it is known that 35% of the students live on campus. The director of student life is going to take a random sample of 200 students. Which of the following is most likely to occur.
Select one:
The sample proportion falls between 0.15
The sample proportion falls between 0.25 and 0.45 (q3)
At North Carolina State University it is known that 56% of undergraduates are male. If a sample of 160 undergraduate students was taken, which of the following would accurately describe the sampling distribution?
Select all that apply.
Select one or more:
The sampling distribution will be approximately normal. The mean of the sampling distribution will be equal to 56%. The standard deviation of the sampling distribution will be 0.0392. (q3)
Which of the following scenarios would it be appropriate to use normal approximation for the sampling distribution of the proportion?
Select all that apply.
Select one or more:
A researcher wishes to find the probability that less than 25% of a sample of
A researcher wishes to find the probability that less than 25% of a sample of undergraduate students from Winston Salem State University will be male. He randomly samples 42 undergraduate students from the student database. The population proportion of un
A large company knows that 7% of their employees are paid sales commissions as part of their compensation. The director of human resources is going to take a random sample of 25 employees to complete a survey about compensation. What do we know about the
It will be somewhat skewed to the right. (q3)
Some IQ tests are standardized to a Normal model, with a mean of 100 and a standard
deviation of 16.
a) About what percent of people should have IQ scores below 72?
b) About what percent of people should have IQ scores between 68 and 84
c) About what perc
Unti 3 Practice Problems
a) 0.0401
b) 0.1359
c) 0.1587
In a really large bag of M&M's, students randomly selected 500 candies, and 12% of them
were green. Note: There are 6 different colors of M&M's in each bag, and the company
claims that each color is equally likely.
a) Is it appropriate to use a Normal mod
Unit 3 Practice Problems
a) Note first, that the probability of selecting a green M&M is 1
6 = 0.167. Then, n ? p =
500 ? 0.167 = 83.3 ? 10 and n ? q = 500 ? 0.833 = 416.7 ? 10. Therefore, we have
satisfied the 'Rule of Thumb'
b) Because we know that norm
Information on a packet of seeds claims that the germination rate is 92%. What's the
probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to
discuss any assumptions that you make and check the conditions that support your
Unit 3 Practice Problems
First we need to assume that this is a random sample. Additionally, we need
to check the 'Rule of Thumb' to see if a Normal distribution would be appropriate. Here
n ? p = 160 ? 0.92 = 147.2 ? 10 and n ? q = 160 ? 0.08 = 12.8 ? 10
It's believed that 4% of children have a gene that may be linked to juvenile diabetes.
Researchers hoping to track 20 of these children for several years test 732 newborns for the
presence of this gene. What's the probability that they find at least 20 su
Unit 3 Practice Problems Solution First, we need to check the 'Rule of Thumb' to see if a Normal distribution would
be appropriate. Here n ? p = 732 ? 0.04 = 29.28 ? 10 and n ? q = 732 ? .96 = 702.72 ? 10.
Therefore a Normal distribution is appropriate. A
A company's customer service hotline handles many calls relating to orders, refunds, and
other issues. The company's records indicate that the median length of calls to the hotline
is 4.4 minutes with an IQR of 2.3 minutes.
a) If the company were to descr
Unit 3 Practice Problems
a) Median: 264 seconds, IQR: 138 seconds
b) Median: 240 seconds, IQR: 138 seconds
When engineers design products, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, we can assume the weight of adult males in the US has a mean weight of 197 p
0.67 (q4)
In psychology, there is a particular Mental Development Index (MDI) used in the study of infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children a
.9772 (q4)
A west-coast tech company knows the average age of its employees is 34 years. They also know that the standard deviation of the ages of these employees is 8 years. We know that the population of employee ages will have a right skewed distribution. A manag
We know that the shape of the sampling distribution of the mean will be approximately symmetric. The sampling distribution of the mean will have a smaller standard deviation than the population. (q4)
According to the most recent census, the average income of households in Wake County is $58,500. It is also known that the distribution of household income in Wake County is strongly skewed to the right with a standard deviation of $14,000. A researcher i
The sampling distribution of the mean will have a smaller standard
We know that the shape of the sampling distribution of the mean will be right skewed. (q4)
For each of the following, tell whether the population parameter of interest is � or p.
The U.S. Bureau of Labor and Statistics sampled fifty people in Arkansas asking them their age. Their average age is 49.4 years old with a standard deviation of 17.1 y
m,p,m (q4)
At a large university it is known that 40% of the students live on campus. The director of student life is going to take a random sample of 200 students. What is the probability that more than half of the sampled students live on campus?
Give your answer
.0019 (q4)
According to a recent report the average income of all people in Adair County Missouri is
$31,023. Which of the following is more likely? Pick one and explain.
(a) We take a random sample of 50 people from this county and find that the average is
over $50
Unit 4
(a) With smaller sample sizes, there is more sampling variability, so we would be more
likely to observe extreme values of a sample mean.
Statistics from Cornell's Northeast Regional Climate Center indicate that Ithaca, NY, gets
an average of 35.4" of rain each year, with a standard deviation of 4.2". Assume that a
Normal model applies.
(a) During what percentage of years does Ithaca get mo
unit 4
(a) 0.1357
(b) 31.872
For each of the following items, write the proper formula for the standard score. Refer to
the formulas on the Formula Sheet. Note: Just write out the proper formula including all
the appropriate values as if you were going to calculate the standard score
unit 4
(a) z =
y�?�
?/
?
n
=
70?63
4/45
(b) z = ?
p�?p
pq
n
= ?.5?.75
.75�.25
100
(c) z =
y?�
?
=
95?90
The weight of potato chips in a medium-size bag is stated to be 10 ounces. The amount
that the packaging machine puts in these bags is believed to have a Normal model with
mean 10.2 ounces and standard deviation 0.12 ounces.
(a) Can we estimate the the pr
unti 4
a. = 0.0475.
b. 0.0019
c. =0
The finishing times of a 10k race are believed to have a skewed right population with mean
59 minutes with a standard deviation of 8 minutes.
(a) Can we estimate the probability that a runner will beat her goal time of 45 minutes?
If so, calculate the pro
unit 4
(a) No, parent population is skewed and therefore NOT Normal.
(b) No, since the parent population is skewed we need a sample size of at least 30 to use
the CLT. Thus, the sampling distribution is NOT Normal.
(c) Yes, since we took a random sample a
A university expects that the proportion of all undergraduate students enrolled who own
a laptop is .70.
(a) If we were to take a random sample of 10 undergraduate students, can we estimate the
probability that less than half of the students sampled own a
unit 4
(a) No, we must have np ? 10 and nq ? 10, but nq = 10 ? 0.3 = 3 < 10.
(b) Yes, we have a random sample and np = 45?0.7 = 31.5 ? 10 and nq = 45?0.3 = 13.5 ? 10,
so we can use the Normal distribution. P(p� > 0.75) = P
?
?
?
p�? 0.7
?0.7?0.3
45
>
0.75
in a specific, mid-size, warm-weathered city in southern California, there are 2 million homes. As part of an environmental status survey, it was desired to estimate the proportion of homes in this city which contain lead based paints. A simple random sam
.264 (q5)
The CEO of a large corporation asked her head HR representative to take a random sample of 97 employees. From his sample, he finds that the proportion of their employees that have children is 0.85. What is the standard error of the proportion in this situ
.036 (q5)
Elon Musk is working on a new hybrid engine designed specifically for SUV's and he wants to know how these engines would sell in Orange County, California. As such, he wants to estimate the proportion of cars in Orange County, California that would be con
- Decrease compared to the interval above
- increase compared to the interval above
- increase compared to the interval above
-decrease compared to the interval above
A political action committee wanted to estimate the proportion of county residents who support the installation of red light cameras throughout the county. They took a random sample of 600county residents and found that the proportion who wanted to instal
We believe that the true proportion of county residents who want the law changed is between 28% and 36%. (q5)
A sample of 900 high school seniors were randomly selected for a national survey. Among the survey participants, 372 students were interested in pursuing a liberal arts degree within the next year. The sample proportion is 0.413.
What is the margin of err
~ .027
~ .386
(q5)
In which of the following scenarios would it be appropriate to construct a 95% confidence interval for the parameter of interest?
Select all that apply.
Select one or more:
A state safety official wants to estimate the proportion of licensed cars in NC th
A state congressman wants to know the proportion of NC voters who support higher taxes to pay for state parks. He randomly selects 200 voters, and he asks them if they support higher taxes for state parks. 15% of the selected voters supported the higher t
True or false:
A 95% confidence interval means that 95% of all sample statistics will be in our interval.
Unit 5
false. A correct statement is "A 95% confidence interval means we
believe the PARAMETER is within our interval". Remember, we use the statistic to learn
about the parameter, because the parameter is ultimately what we are interested in.
True or false:
The confidence level is an expression of our confidence in the procedure that was used to
create the interval of interest.
unit 5
s true. "A 95% confidence level means that using the same procedure
repeatedly on different samples of the same size, about 95% of the intervals will contain
the parameter".
True or false:
A larger sample size will produce a larger margin of error.
unit 5
false because a larger sample size will produce a smaller margin of error.
True or false:
A higher level of confidence will produce a larger margin of error.
unit 5
true because a higher level of confidence corresponds to a larger standard
score (draw a picture to see this). Intuitively, to have more confidence that our interval
contains the parameter, the interval needs to include more values.
An institution that ranks colleges and universities along several dimensions is interested in
learning the proportion of undergraduate students at Mid-South State University who have
had at least one alcoholic drink in the past week. The institution rando
unit 5
(a) The standard error of �p is qp�q�
n =
q(.38)(1?.38)
100 =
q(.38)(0.62)
100 = 0.049. This is an
estimate of the variability of the sampling distribution for the sample proportion.
(b) The conditions are that we need a large, random sample. We ar
FirstUSA, a major credit card company, is planning a new offer for their current cardholders.
The offer will give double airline miles on purchases for the next 6 months if the
cardholder goes online and registers for the offer. To test the effectiveness
unit 5
a) �p =
1184
50000 = 0.024, so the confidence interval is �p � z
qp�q�
n ? .024 � 1.96q
.024�.976
50000 =
.024 � .00133 = (.0227, .0253). We believe the true percent of cardholders who will
register for the offer is between 2.27% and 2.53%.
b) Sinc
Direct mail advertisers send solicitations (a.k.a. "junk mail") to thousands of potential
customers in the hope that some will buy the company's product. The acceptance rate is
usually quite low. Suppose a company wants to test the response to a new flyer
unti 5
a) �p =
123
1000 = 0.123 , so the confidence interval is �p � z
qp�q�
n ? .123 � 1.64q
.123�.877
1000 =
.123 � .017 = (.106, .140)
b) We believe that the percentage of people the company contacts who buy something is
between 10.6% and 14%.
c) If we
True or false:
A t statistic is used to construct confidence intervals for means in order to account for
additional uncertainty in estimating the standard deviation.
unit 6
true
True or false:
We use a t distribution to calculate the margin of error for sample proportions.
unti 6
false, When calculating confidence intervals for proportions,
we use a normal distribution.
Find the appropriate t multiplier for the following situations:
a) A 95% confidence interval with n = 8
b) A 99% confidence interval with n = 11
unti 6
a) n = 8 ? df = n ? 1 = 7, so t = 2.365
b) n = 11 ? df = 10, so t = 3.169
A demographer recently collected a random sample of 25 people to find out the average
number of children that households in Durham, NC have. It is believed that the population
has a normal distribution. They found the average value of their sample was 2.4
unti 6
(a) Standard error = s
?
n
=
1
?
25
= 0.2
(b) tn?1 = t24 = 2.064
(c) Margin of error = t � ?s
n = 2.064 � 0.2 = 0.413
(d) A random sample was used and the distribution of the population is normal (which
is needed since n = 25 < 30), which are both
What standard score (z
?
) has 4.95% of values above it?
unit 6
z = 1.65
An undergraduate French instructor gives an exam, and the exam scores are lower than he
had hoped. He decides to curve the scores by adding 10 points to everyone's exam score.
Which of the following will be affected by the curve:
a) Mean
b) Standard devia
unit 6
a) Mean: Yes
b) Standard deviation: No, the standard deviation is not affected by adding the same value
to everyone's score, as addition (and subtraction) simply shift the distribution along the
number line but do not change the shape.
c) IQR: No,
Software analysis of the salaries of a random sample of 288 Nevada teachers produced the
90% confidence interval of ($38, 944, $42, 893). Which statement(s) is(are) correct? What's
wrong with the other(s)?
a) If we took many random samples of 288 Nevada t
unit 6 a) Ninety percent of the intervals will contain the true mean salary; different samples will
produce different intervals.
b) This is correct.
Page 2
ST 311 Evening Problem Session - Solutions Week 6
c) The interval is for the population mean, not i
Public relations staff at State U. phoned 850 randomly selected local residents. After
identifying themselves, the callers asked the survey participants their ages, whether they
had attended college, and whether they had a favorable opinion of the univers
unit 6
a) i. Age - Quantitative - Mean
ii. College Attendance - Categorical - Proportion
iii. Favorable Opinion of the University - Categorical - Proportion
b) From the prompt, �p =
650
850 = 0.76. The 95% confidence interval is as follows:
p�� z �
r
p� �
Hoping to lure more shoppers downtown, a city builds a new public parking garage in
the central business district. The city plans to pay for the structure through parking fees.
During a two-month period (41 weekdays), daily fees collected averaged $126, w
unit . 6
(a) The 90% confidence interval is as follows:
y� � t �
s
?
n
? 126 � 1.684 �
15
?
41
? 126 � 3.94 ? (122.06, 129.94)
(b) The interval provides us with a range of reasonable values for the true average, and
since the interval does not contain the
Sony is interested in estimating the proportion of US households that have Blueray players.
A researcher randomly selects 500 households, and discovers 115 own Blueray players.
[Learning Objectives A1, A4, E5]
a) What is the population? The parameter of i
unit 6 a) The population is all US households. The parameter of interest is the proportion of
US households that own Blueray players.
b) A simple random sample is used. The sample size is 500.
c) The sample proportion �p =
115
500 = 0.23.
Page 4
ST 311 Ev
We are interested in the average height of 5 year old children, so we did a survey. The
resulting data (in inches) are 24, 26, 34, 38, 29, 33. The sample mean is 30.7 and the
sample standard deviation is 5.3. [Learning Objectives C4, D6, E10, F16, F18]
a)
a) They would both increase by a factor of 2.5 because multiplication (or division) affects
both measures of center and measures of spread. Mean: 30.7 � 2.5 = 76.75cm, SD:
5.3 � 2.5 = 13.25cm.
b) z =
34?32
3 = 0.67. Looking this up on the Z table we find
Researchers who examined health records of thousands of males found that men who died
of myocardial infarction (heart attack) tended to be shorter than men who did not.
a) Is this an observational study or an experiment?
b) What is the explanatory variabl
unit 7
a) This is an observational study because it's not manipulating any of the variables. They
are using previously collected data and considering relationships between the variables.
b) The explanatory variable is height. This could be either quantita
When spending large amounts to purchase advertising time, companies want to know what
audience they'll reach. In January 2007, a poll asked 1008 randomly selected American
adults whether they planned to watch the upcoming Super Bowl. Men and women were
as
unit 7
a) This is a stratified sample. The question was about population values (the proportions
of men and women who look forward more to the commercials). There was no treatment
applied or manipulation of explanatory variables, so it is not an experimen
Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee,
but many people cheat. On randomly selected days, researchers at Newcastle University
replaced the picture of flowers on the wall behind the coffee station w
unit 7
a) This is an experiment.
b) The explanatory variable is picture that was used. This is a categorical variable.
c) The response variable is the average amount that was contributed. This is a quantitative
variable.
d) Yes, by randomly selecting the
Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts
can help alleviate the problem, while others recommend exercise. Forty volunteers suffering
from insomnia agreed to participate in a month-long test. Half were ran
unit 7
a) This is an experiment.
b) The explanatory variables are desserts and exercise (each with 2 levels). They are each
categorical.
c) The response variable is improvement in insomnia. Depending on how insomnia is measured,
it could be either categor
Some people who race greyhounds give the dogs large doses of vitamin C in the belief that
the dogs will run faster. Investigators at the University of Florida tried three different diets
in random order on each of five racing greyhounds. They were surpris
unit 7
a) This is an experiment.
b) The explanatory variables is the diet. There are three different levels of the factor. This
is a categorical variable.
c) The response variable is the dog's racing speed.
d) This is a matched design since each dog tried
A swimsuit manufacturer wants to test the speed of its newly designed suit. The company
designs an experiment by having 6 randomly selected Olympic swimmers swim as fast as
they can with their old swimsuit first and then swim the same event again with the
Unit 7
a) The explanatory variable here is swimsuit type. It is a categorical variable.
b) The response variable is the swimmer's racing speed. It is quantitative.
c) This is a matched pairs design since each subject (swimmer) underwent both treatments.
d
An experiment showed that subjects fed the DASH diet were able to lower their blood
pressure by an average of 6.7 points compared to a group fed a "control diet." All meals
were prepared by dietitians.
a) Why were the subjects randomly assigned to the die
unit 7
a) Self-selection could systematically introduce lurking variables, resulting in groups that
were very different at the start of the experiment, making it impossible to attribute the
differences in the results to their diet.
b) This assured that al