Download MATH-138 In-class Practice Problems Written by Dr. Gregory

MATH-138 In-class Practice Problems
Written by Dr. Gregory Coldren, Mathematics Division, Howard Community College
1. Suppose a basketball player scored the following number of points in his last 15
games: 4, 4, 3, 4, 7, 16, 12, 23, 15, 8, 5, 18, 8, 29, 21.
Fill in the following frequency (and relative frequency) distribution.
Bin
1-6
7-12
13-18
19-24
25-30
Total
Frequency
5
4
3
2
1
Relative Frequency
33%
27%
20%
13%
7%
2.
a.
b.
What percentage of games did the player score 12 points or less?
What percentage of games did the player score between 7 and 18 points
(inclusive i.e. 7 < points < 18)?
3.
If you were to draw a histogram from your frequency distribution (from Question
1), would it be skewed to the right or left? That is, is this distribution skewed right
or left?
4.
Calculate the following statistics from the basketball scores: Mean, Median,
Quartile 1, Quartile 3, Minimum, Maximum, Range, IQR, and Standard
Deviation.
5.
Construct a boxplot for the above-mentioned basketball scores.
6.
Use the above-mentioned basketball scores to calculate the z-scores for the 3
lowest-scoring and 3 highest-scoring games.
7.
A college student received a score of 78 on her Math exam and a score of 86 on
her French exam. The overall results on the French exam had a mean of 82 and a
standard deviation of 8, while the math exam had a mean of 54 and a standard
deviation 12. On which exam did she do relatively better?
8.
Who is relatively taller:
A. A non-basketball playing man who is 75 inches tall (assume nonbasketball playing men have a mean height of 71.5 inches tall and a
standard deviation of 2.1 inches).
B. A male basketball player who is 85 inches tall (assume male basketball
players have a mean height of 80 inches and a standard deviation of 3.3)
9.
Assume verbal SAT scores have a mean of 500 and a standard deviation of 100.
What is the z-score of somebody who scores 500 on the verbal portion of the
SAT?
10.
Assume IQ scores have a mean of 100 and a standard deviation of 16. Albert
Einstein reportedly had an IQ of 160. What is the z-score of his IQ?
Assume IQ scores have a normal model distribution with a mean of 100 and a standard
deviation of 16. Use this information to answer Questions 11-14.
11.
Find the following percentages:
a.
% of people with 84 < IQ < 116
b.
% of people with IQ > 100
c.
% of people 68 < IQ < 132
d.
% of people who are “geniuses” (a genius is someone with an IQ > 132)
e.
% of people 84 < IQ < 132
12.
Find the following percentage:
a.
% of people with IQ < 125
b.
% of people with 90 < IQ < 110
c.
% of people with 110 < IQ < 120
13.
What value (IQ score) separates the bottom/lower/not-so-smart 10% of the
population from the top/upper/smarter 90%?
14.
What value (IQ score) separates the top/smarter 35% of the population from the
bottom/not-so-smart 65%?
Suppose the IQ scores of people who smoke copious amounts of pot are normally
distributed with mean=90 and standard deviation=20 (assume IQ scores are continuous
and not necessarily integers). Suppose the IQ scores of people who don’t smoke copious
amounts of pot are normally distributed with mean=100 and standard deviation=16. Use
this information to answer Questions 15-18.
15.
Find the following percentages:
a.
A former psychological classification of mental retardation labeled
someone with an IQ score between 50 and 68 as a “moron”. What
percentage of copious pot smokers are “morons”?
b.
What percentage of non-copious pot smokers are NOT “morons”?
c.
What percentage of copious pot smokers have an IQ score within 1
standard deviation of the mean?
d.
What percentage of non-copious pot smokers have IQ scores within 2
standard deviations of the mean?
16.
Find the following percentages:
a.
The percentage of non-copious pot smokers who have an IQ score higher
than the mean of copious pot smokers?
b.
The percentage of non-copious pot smokers who are geniuses (a “genius”
is somebody with an IQ of 132 or higher)?
17.
What is the IQ score of the following people (round to the nearest integer):
a.
A copious pot smoker who is smarter than 90% of all the other copious pot
smokers.
b.
A non-copious pot smoker who is dumber than 90% of all the other noncopious pot smokers
18.
What IQ score will separate the smarter half of the copious pot smokers from the
dumber half?
19.
The following data represent movie budgets vs. gross revenue (in million $) for 7
movies. Create a scatterplot to see if r should be calculated. If so, what is r (Triola
2008)?
Budget
62
90
50
35
200
100
90
Gross
65
64
48
57
601
146
47
20. The following data represent supermodel heights (inches) vs. weights (pounds) for 9
supermodels. Create a scatterplot to see if r should be calculated. If so, what is r (Triola
2008)?
Height
70
70.5
68
65
70
70
70
70
71
Weight
117
119
105
115
119
127
113
123
115
21.
a.
b.
c.
d.
Estimate the regression equation for Question #19 (use budget as
your independent, “x” variable)
Interpret the slope and intercept in the context of this problem
How much gross revenue does the regression line predict a movie with a
$95 million budget will make?
What is the residual for the movie in the data that had a $100 million
budget?
22.
A basketball player makes 80% of her free throws. Suppose she wakes up every
morning and starts shooting free throws. On an “average” morning, on which free
throw will she have her first miss? Perform 20 trials.
23.
You are going to take a quiz with 5 multiple choice questions. You estimate that
you have a 80% chance of getting any question right. What are you chances of
getting them all right? Perform 20 trials.
24.
You are going to take a quiz with 10 multiple choice questions, where each
question has 4 answer choices. You have not studied and you need to guess on
each question. What are your chances of passing the quiz (i.e. getting at least 6
out of 10 questions correct on the quiz)? Perform 20 trials.
25.
Suppose we wanted to study how many credit hours HCC students are taking this
semester. How would we get a simple random sample (SRS) of HCC students?
Stratified sample? Cluster sample? Systematic sample? Convenience sample?
Census?
26.
Which of the following (if any) are NOT valid probability values?
a.
0.40
b.
-0.20
c.
1.00
d.
0.99999
27.
Which of the following (if any) are NOT valid probability values?
a.
0.00
b.
0.67
c.
0.80
d.
1.14
Suppose I want to perform the random procedure of rolling a fair die (rolling it once).
Use this procedure to answer Questions 28-34.
28. What is the sample space, S, for the above-mentioned procedure?
Consider the following events:
a.
Rolling a 1
b.
Rolling anything but 6
c.
Rolling something less than 2
d.
Rolling something between 2 and 5, inclusive (i.e. including 2 and 5)
29.
What are the probabilities for the four events listed above?
30.
What are the complements of the four events listed above?
31.
What are the probabilities of the four complements?
32.
State whether each of the following pairs of events (from above) are mutually
exclusive or not:
a.
Events a and b
b.
Events a and c
c.
Events b and d
d.
Events c and d
33.
For the above die-rolling example, give an example of an impossible event.
34.
For the above die-rolling example, give an example of a certain event.
The table below describes a standard deck of cards. Use the table to answer Questions 3536. Note that I am counting aces as face cards.
35.
State whether each of the following pairs of events are mutually exclusive or not:
a.
Black cards and red cards
b.
Black cards and diamonds
c.
Black cards and spades
d.
Diamonds and face cards
e.
Face cards and non-face cards
f.
Non-face cards and red cards
36.
Suppose I want to perform the random procedure of picking a card out of a0
standard deck of cards. If ONE card is drawn, what are the following probabilities
(please answer using un-simplified fractions):
a.
P(club)
b.
P(not a heart)
c.
P(face card)
d.
P(red)
e.
P(not a non-face card)
f.
P(not black)
g.
P(black or red)
37.
One tie – dotted, striped, or solid – is selected at random, and then a shirt – white
or brown – is selected at random. What is the probability that a dotted tie AND
white shirt are selected?
a.
1/6
b.
1/2
c.
1/3
d.
3
e.
None of these
38.
What is the probability that you roll a die 4 times and get zero “6’s”?
39.
What is the probability that you roll a die 4 times and get at least one “6”?
40.
What is the probability that someone who has 3 children has exactly one girl
(assume no twins, triplets, or hermaphrodites)?
41.
What is the probability that you flip a coin twice and get 2 tails?
42.
What is the probability that you flip a coin 10 times and the seventh flip is heads?
The table below describes a standard deck of cards. Use the table to answer Question 43.
Note that I am counting aces as face cards.
Face Cards Non-Face Cards
4
9
Clubs (black)
4
9
Spades (black)
4
9
Hearts (red)
4
9
Diamonds (red)
43.
Suppose I want to perform the random procedure of picking a card out of a
standard deck of cards. If ONE card is drawn, what are the following probabilities
(please answer using un-simplified fractions):
a.
P(face card and black)
b.
P(red or non-face card)
c.
P(face card or not black)
d.
P(black and red)
e.
P(club or face card)
f.
Given the card is black, what is P(club)?
g.
Given the card is black, what is P(face card)?
h.
Given the card is a non-face card, what is P(face card)?
Use the data on the next page to answer Question 44. This synthetic sample data (i.e. I
made it up) shows 1,000 people who either smoked or didn’t smoke, and who either died
of lung cancer or some other cause of death. Suppose I randomly sample one person from
this data.
Smoker
Non-Smoker
Lung Cancer Death
50
80
Non-Lung Cancer Death
150
720
44.
a.
b.
c.
d.
e.
f.
g.
What is P(Smoker)?
What is P(Lung Cancer Death)?
What is P(Smoker given Lung Cancer Death)?
What is P(Non-Lung Cancer Death)?
What is P(Non-Smoker)?
What is P(Non-Lung Cancer Death given Non-Smoker)?
Is smoking and lung cancer death independent?
45.
Given P(A)=0.25, P(B)=0.60, and P(A and B)=0.10, find:
a.
P(A or B)
b.
P(B|A)
c.
Are A and B independent (yes or no)?
d.
Are A and B mutually exclusive (yes or no)?
46.
One tie – dotted, striped, or solid – is selected at random, and then a shirt – white
or brown – is selected at random. What is the probability that a striped tie OR
brown shirt is selected?
a.
1/2
b.
2/3
c.
1/6
d.
5/6
e.
None of these
47.
Suppose TWO fair dice are rolled. Find the following probabilities:
a.
P(both die are 1)
b.
P(the sum of the dice is 6)
c.
P(at least one of the dice is 4)
d.
P(only ONE of the dice is 4)
48.
Suppose TWO fair dice are rolled. Let E be the event of getting a “triple” (i.e. one
die is three times the other die) and let F be the event of getting a “sum of 6” (i.e.
the two dice add up to 6). Which one of the following statements is true:
P(E)>P(F), P(E)=P(F), or P(E)<P(F)?
49.
Suppose a dresser drawer contains 20 individual socks where each sock is either
white or black (there is at least one of each color). Suppose you are blindfolded
and you start taking out socks from the drawer one by one. What is the
MINIMUM number of socks that you need to take out in order to GUARANTEE
that you will have some matching socks (i.e. 2 black socks OR 2 white socks).
50.
For parts a-c below, state whether the pairs of events (events A and B) are
dependent or independent:
a.
P(A)=0.60, P(B)=0.40, P(A and B)=0.24
b.
P(A)=0.90, P(B)=0.30, P(A and B)=0.18
c.
P(A)=0.50, P(B)=0.70, P(A and B)=0.25
51.
Suppose a jar contains 40 red marbles, 40 blue marbles and 20 green marbles (100
marbles total). If TWO marbles are drawn WITHOUT REPLACEMENT from the
jar (that is, one marble is drawn and NOT put back into the jar, and then another
marble is drawn), what are the following probabilities?
a.
P(both are green) (i.e. the first marble is green AND the second marble is
green)
b.
P(neither are green)
c.
P(first marble is red)
d.
P(first marble is red, second marble is blue)
e.
P(both marbles are neither red nor green)
f.
P(first marble is red, second marble is green)
g.
Given the first marble is red, what is P(second marble is red)?
h.
Given the first marble is green, what is P(second marble is blue)?
52.
If TWO cards are drawn WITH REPLACEMENT from a standard deck of cards
(that is, the first card is put back into the deck (and the deck is shuffled) before the
second card is drawn), what are the following probabilities?
a.
P(both are black) (i.e. the first card is black AND the second card is black)
b.
P(first card drawn is red, second card drawn is black)
c.
P(both cards are neither red nor face cards)
d.
P(first card drawn is a red face card, second card drawn is red)
e.
Given the first card drawn is a red card, what is P(second card is red)?
f.
Given the first card drawn is a club face card, what is P(second card is a
diamond face card)?
53.
Give the probabilities for Questions #52A-F assuming the two cards are drawn
WITHOUT REPLACEMENT (that is, one card is drawn and NOT put back into
the deck, and then another card is drawn) and the deck is shuffled after
replacement.
54.
In Question #52, does the probability of the second draw depend on the first
draw?
55.
In Question #53, does the probability of the second draw depend on the first
draw?
56.
A large department store has 500 employees. There are 350 females and 200 of
them are under the age of 25. There are 75 males under 25. If one employee is
randomly selected, what are the following probabilities:
a.
P(under 25 or female)
b.
P(over 25 or female)
c.
P(male or over 25)
57.
There are 6 green hats, 4 blue hats and 3 red hats in a box. You randomly select
one hat. What are the following probabilities:
a.
P(blue or red)
b.
P(not green)
c.
P(green or blue or red)
58.
In a class of 50 students, 18 take chorus, 26 take band, and 2 take both. Answer
the following questions:
a.
How MANY are only in chorus?
b.
How many are only in band?
c.
How many take neither?
d.
How many take either band or chorus (but NOT both)?
In Questions 59 – 61, do the tables given represent a valid probability distribution?
Explain why or why not.
59.
60.
X
-3
-1.56
2
5.7
10,002
P(x)
0.20
0.10
0.05
0.56
0.09
61.
X
4
6
8
9
P(x)
-0.50
0.60
0.50
0.40
X
0
1
P(x)
0.45
0.65
Suppose a random procedure that yields the following outcomes and probabilities. Use
this table to answer Questions 62-63.
X
80
100
150
200
250
P(x)
0.24
0.22
0.31
0.18
0.05
62.
Find the mean (expected value) and standard deviation of this distribution.
63.
What are the following probabilities:
a.
P(X < 150)
b.
P(X = 200)
c.
P(X < 70)
d.
P(X = 100 or X = 200)
e.
P(X = 100 and X = 250)
f.
P(X < 200 or X > 80)
64.
Suppose I have a distribution where one third of the time the value equals -1, one
third of the time the value equals 0, and one third of the time the value equals 2. Is
this a valid probability distribution?
65.
Suppose I have a distribution where one half of the time the value equals 0.4, and
two thirds of the time the value equals 0.6. Is this a valid probability distribution?
Use the following table to answer Questions 66-67:
X
0
1
2
3
10
P(x)
0.0
0.3
0.3
0.3
0.1
66.
Why is this probability distribution valid?
67.
Find the expected value and standard deviation of this distribution.
68.
A carnival game offers a $100 cash prize for anyone who can break a balloon by
throwing a dart at it. It costs $5 to play. You estimate that you have a 10% chance
of hitting the balloon on any throw. Find your expected winnings.
69.
(De Veaux et al. 2009) A commuter must pass through 5 traffic lights on her way
to work and will have to stop at each one that is red. She estimates the probability
model for the number of red lights she hits as shown below.
X=# of red
0
1
2
3
4
5
0.05 0.25 0.35 0.15 0.15 0.05
P(x)
How many red lights should she expect to hit each day? 2.25
70.
An insurance policy has the following pay offs. If you die, your survivor gets
$10,000. If you become disabled, you get $5000. Otherwise, you receive nothing.
The policy costs $50 a year. Based on past data, the probability a person dies is
.01 and the probability the person becomes disabled is .02. Find the expected
value from your point of view.
71.
(De Veaux et al. 2009) You roll a die. If it comes up 6, you win $100. If not, you
get to roll again. If you get a 6 the second time, you win $50. If not, you lose.
Create the probability model and find the expected amount you’ll win. How much
should you pay to play this?
72.
A game costs $5 to play. You draw a card from a deck of cards. If you draw the
ace of hearts, you win $100. For any other ace, you get $10 and for any other
heart you get $5. If you draw anything else, you lose. Find the average winnings
or losses for this game.
73.
Suppose you visit Las Vegas and decide to play roulette. If you bet $5 that the
outcome is a number between 1-12 (including 1 and 12), you have a 26/38
probability of losing your $5 bet, and you have a 12/38 probability of making a
net gain of $10 (equaling the $15 prize minus your $5 bet). Only considering NET
winnings/losses, what is your expected value of betting on a number between 112 (round to the nearest cent)?
74.
A man buys a racehorse for $20,000 and enters it in two races. He plans to sell the
horse afterwards hoping to make a profit. If the horse wins both races, it will sell
for $100,000. If it wins only one race, it will be worth $50,000. If it loses both
races, it will be worth $10,000. The man believes there is a 20% that the horse
will win the first race and a 30% chance that it will win the second race.
Assuming the two races are independent events, find the man’s expected profit.
75.
Suppose the following binomial probability situation: A certain statistics class has
15 students, and the probability that a given student will pass the class is 0.8. Find
the following probabilities:
a.
P(everybody passes)
b.
P(at least 10 students pass)
c.
P(4 students fail)
d.
P(11 or 12 students pass)
e.
P(at most 2 students fail)
76.
Suppose the following binomial probability situation: You draw a card out of a
shuffled deck of cards 10 times (replacing the card after each draw and reshuffling) and count the number of red cards you draw (note there are 26 red
cards and 52 cards total). Find the following probabilities (3 decimal places):
a.
P(6 red cards)
b.
P(3 black cards)
c.
P(at most 5 red cards)
d.
P(more than 7 black cards)
77.
A moving target at a police academy target range can be hit 80% of the time by a
particular individual. Suppose the person takes three shots at the target. What is
the probability that:
a.
There are exactly two hits?
b.
There are hits on all three?
c.
There is only one hit?
d.
There are misses on all three?
e.
There is at least one hit?
78.
A quality control inspector has drawn a sample of 13 light bulbs from a recent
production lot. If the number of defective bulbs is 2 or less, the lot passes
inspection. Suppose 10% of the bulbs in the lot are defective. What is the
probability that the lot will pass inspection?
79.
Suppose the following binomial probability situation: Suppose Dr. Coldren was a
single male. Further suppose that there was a week in the distant past (SundaySaturday) where he asked a different supermodel for a date (for that evening) each
day of the week. Suppose the probability that any given supermodel said “yes”
was 0.20. Assume a supermodel agreeing to a date was a “success”, and not
agreeing to a date was a “failure” (meaning I stayed home alone for the evening).
Find the following probabilities:
a.
P(Dr. Coldren stayed home alone all week) 0.210
b.
P(Dr. Coldren had dates with supermodels only on days that began with
“S”)
c.
P(Dr. Coldren stayed home alone at least one evening)
d.
P(Dr. Coldren had a date with a supermodel every evening of the week)
e.
P(Dr. Coldren was home alone an odd number of evenings)
80.
Public health statistics indicate that 26.4% of American adults smoke. Describe
the sampling distribution for a sample of 50 adults.
81.
Assume that 30% of the students at a certain community college wear contact
lenses and we randomly pick 100 students to see what percentage of them wear
contacts. Describe this sampling distribution. What is the probability that more
than one third of them wear contacts?
82.
It is 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 they find
enough subjects for the study?
83.
A restaurateur anticipates serving 180 people on a Friday evening and believes
that about 20% of the patrons will order the steak special. How many of those
specials should he plan on ordering in order to be 95% sure (i.e. only a 5% chance
of running out of food) of having enough steaks on hand to meet customer
demand?
84.
A college’s data about the incoming freshmen indicates that the mean of their
high school GPAs is 3.4 with a standard deviation of 0.35. The distribution is
normal. The students are randomly assigned to freshmen writing seminars in
groups of 25.
a.
Find the probability a given student has a GPA greater than 3.5.
b.
Find the probability that one of the groups has an average GPA greater
than 3.5.
85.
Ithaca, New York gets an average of 35.4” of rain each year with a standard
deviation of 4.2”. Assume the Normal model applies to their yearly rainfall.
a.
What percentage of years does Ithaca get more than 40” of rainfall?
b.
What rainfall amount separates the “driest” 20% of years from the
“wettest” 80%?
c.
Suppose you live in Ithaca for four consecutive years. What is the
probability that those four years average less than 30” of rain?
86.
Suppose the weights of men are normally distributed with a population mean of
180 pounds and a population standard deviation of 20 pounds. Suppose a crew of
10 men are about to board a fishing boat. Further suppose the boat can safely
carry 10-person crews weighing less than 1900 pounds total (i.e. safely carry 10person crews where the average crew member weighs less than 190 pounds).
Suppose the above-mentioned 10 male crew members were randomly sampled
from the overall population of men. Use this information to answer the following:
a.
What is the probability that any one of the crew members weighs more
than 190 pounds?
b.
What is the probability that the entire crew weighs more than 1,900
pounds – and hence a catastrophe is likely to occur?
Hint: In other words, what is the probability that the AVERAGE weight of the
crew members is more than 190 pounds?
87.
A poll found that 50% of a random sample of 1012 American adults said that they
believe in ghosts.
a.
Find the margin of error for this poll if we want 90% confidence in our
estimate of American adults who believe in ghosts.
b.
Explain what a “90% confidence interval” means and find the interval.
c.
If we want to be 99% confident, will the margin of error be larger or
smaller?
d.
Find that margin of error.
e.
In general, will smaller margins of error involve greater or less confidence
in the interval?
88.
(De Veaux et al. 2009) Direct mail advertisers send solicitations to thousands of
potential customers in the hope that some will buy the company’s product. The
response rate usually is quite low. Suppose a company wants to test the response
to a new flyer and sends it to 1000 people randomly selected from their mailing
list of over 200,000 people. They get 123 orders from the recipients.
a.
Create a 90% confidence interval for the percentage of people the
company contacts who may buy something.
b.
Explain what the interval means.
c.
The company must decide whether to now do a mass mailing. The mailing
won’t be cost effective unless it produces at least a 5% return. What does
your confidence interval suggest?
89.
A national health organization warns that 30% of the middle school students
nationwide have been drunk. Concerned, a local health agency randomly and
anonymously surveys 110 of the 1212 middle school students in its city. Only 21
of them reported having been drunk.
a.
What proportion of the sample reported having been drunk?
b.
Does this mean that this city’s youth are not drinking as much as the
national data would indicate?
c.
Create a 95% confidence interval for the proportion of the city’s middle
school students who have been drunk.
d.
Is there any reason to believe that the national level of 30% is not true of
the middle school students in this city?
90.
In preparing a report on the economy, we need to estimate the percentage of
businesses that plan to hire additional employees in the next 60 days.
a.
How many randomly selected employers must we contact in order to
create an estimate in which we are 98% confident with a margin of error
of 5%?
b.
Suppose we want to reduce the margin of error to 3%. What sample size
will suffice?
c.
Why might it not be worth the effort to try to get an interval with a margin
of error of only 1%?
91.
Write the null and the alternative hypotheses for the following:
a.
In the 1950’s only about 40% of high school graduates went on to college.
Has the percentage changed?
b.
20% of the cars of a certain model have needed costly transmission work
after being driven between 50,000 and 100,000 miles. The manufacturer
hopes that the redesign of the transmission has solved this problem.
c.
We field test a new flavor of soft drink, planning to market it only if we
are sure that at least 60% of the people like the flavor.
d.
The drug Lipitor is meant to lower cholesterol. Is there evidence to
support the claim that over 1.9% of the users experience flu like symptoms
as a side effect?
e.
According to the US department of Health, 16.3% of Americans did not
have health insurance coverage in 1998. A politician claims that this
percentage has decreased since 1998.
f.
During the past forty years, the monthly rate of return for a particular item
has been 4.2 percent. A store analyst claims that it is different.
92.
In the 1980’s it was generally believed that autism affected about 6% of the
nation’s children. Some people believe that the increase in the number of
chemicals in the environment has led to an increase in the incidence of autism. A
recent study examined 384 children and found that 46 of them showed signs of
some form of autism. Is there strong evidence that the level of autism has
increased (Let alpha=0.05)? Write the hypotheses, check the assumptions, draw
the curve, find the pertinent statistics and critical values, find the p value, state
your conclusion, etc.
93.
During the 2000 season, the home team won 138 of the 240 regular season games.
Is this strong evidence of a home field advantage? (Use an α-level of 0.05)
94.
A personal trainer wanted to know whether the proportion of males 30 to 44 years
old who do not exercise has decreased from 24.9%, the proportion in 1998. He
randomly selects 150 males in that age group and finds that 28 of them do not
exercise. Is there significant evidence that the proportion of males in this age
group that do not exercise has decreased (Use an α-level of 0.05)?
95.
A survey of 430 randomly selected adults found that 21% of the 222 men and
18% of the 208 women had purchased books online. Is there evidence that men
are more likely to make online purchases of books? Use an α-level of 0.05.
96.
Would being part of a support group that meets regularly help people who are
wearing the nicotine patch actually quit smoking? A county health department
tries an experiment using several hundred volunteers who are planning to use the
patch. The subjects were randomly divided into two groups. People in Group 1
were given the patch and attended a weekly discussions meeting with counselors
and others trying to quit. People in Group 2 also used the patch but did not
participate in the counseling groups. After six months 46 of the 143 smokers in
Group 1 and 30 of the 151 smokers in Group 2 had successfully stopped smoking.
Do these results suggest that such support groups could be an effective way to
help people stop smoking? Use an alpha level of 0.05.
97.
When games were sampled from throughout a season, it was found that the home
team won 127 of 198 professional basketball games, and the home team won 57
of 99 professional football games.
(a)
Based on these results, does there appear to be a significant difference
between the proportions of home wins for the two sports?
(b)
What can we conclude about home field advantage for these two sports?
Do the hypothesis test with an α-level of 0.05 (Triola 2008).
98.
A gender selection methodology called “XSORT” yielded the following results
for parents who WANTED a girl: 295 out of 325 babies born using the method
were girls. For those parents who wanted a boy (the “YSORT” method was used
for these parents), 39 out of 51 babies were boys. Perform a hypothesis test with
alpha=0.05 for the difference between the proportions of boys and girls being
born using these gender selection methodologies (Triola 2008).
99.
During an angiogram, heart problems can be examined via a small tube (a
catheter) threaded into the heart from a vein in the patient’s leg. It’s important that
the company who manufacturers the catheter maintain a diameter of 2.00 mm.
Each day, quality control makes several measurements to test the 2.00 mm
standard. Discuss one sided versus two sided test. What would Type I and II
errors be?
100.
Suppose the elapsed time of airline itineraries between Washington, D.C. and is
normally distributed with an unknown population mean and an unknown
population standard deviation. Further suppose that a sample of size 25 (therefore,
n=25 and degrees of freedom=24) was taken and the following statistics were
gotten from the sample: sample mean (ybar) =135 and sample standard deviation
(s) = 40. Construct confidence intervals around the sample mean corresponding to
the following confidence levels (express the lower and upper bounds of the
intervals as integers):
a.
80%
b.
90%
c.
95%
d.
98%
e.
99%
Hint: Your intervals should get wider and wider and should all be centered
around 135.
101.
Suppose the elapsed time of airline itineraries between Washington, D.C. and
Boston is normally distributed with an unknown population mean and unknown
population standard deviation. Suppose we randomly sample 25 itineraries and
the sample average is calculated to be 135 minutes and the sample standard
deviation is calculated to be 40. Further suppose that we want to test the
hypothesis that the true population mean (μ) equals 150 minutes. Conduct 2-sided
hypothesis tests with the following α-levels:
a.
α = 0.20
b.
α = 0.10
c.
α = 0.05
d.
α = 0.02
e.
α = 0.01
102.
(De Veaux et al. 2009) Hoping to lure more shoppers downtown, a city builds a
new public parking garage. The city plans to pay for the structure through parking
fees. During a two month period (44 week days) daily fees collected averaged
$126 with a standard deviation of $15. If a consultant claimed that the average
daily income would be $130, should we reject her claim using an α-level of 0.10
(perform a 2-sided test)?
103.
In 1998, the Nabisco Company announced a “1000 Chips Challenge” claiming
that every 18 ounce bag of Chips Ahoy contained at least 1000 chocolate chips.
Below are the counts of chips in selected bags.
1219
1132
1214
1191
1087
1270
1200
1295
1419
1135
1121
1325
1345
1244
1258
1356
Perform a one-sided test (HA: µ>1000). What does this evidence say about
Nabisco’s claim (Use an α-level of 0.05)?
104.
When consumers apply for credit, their credit is rated using FICO scores. A
random sample of credit ratings is obtained, and the FICO scores are summarized
with these statistics: n=18, ybar=660.3, s=95.9. Use an α-level of 0.05 and do a 2sided hypothesis test to test the claim that the mean credit score (of the general
population) is equal to 700 (Triola 2008).
105.
Different cereals are randomly selected, and the sugar content is obtained for each
cereal, with the results given below for Cheerios, Harmony, Smart Start, Cocoa
Puffs, Lucky Charms, Corn Flakes, Fruit Loops, Wheaties, Cap’n Crunch, Frosted
Flakes, Apple Jacks, Bran Flakes, Special K, Rice Krispies, Corn Pops, and Trix.
Use an alpha of 0.05 to test the claim of a cereal lobbyist that the mean of all
cereals is LESS than 0.3 g (Triola 2008).
0.03 0.24 0.30 0.47 0.43 0.07 0.47 0.13
0.44 0.39 0.48 0.17 0.13 0.09 0.45 0.43
106.
A study was conducted to assess the effects that occur when children are exposed
to cocaine before birth. 190 children born to cocaine users had a mean score of
7.3 (with a standard deviation of 3.0) on a certain aptitude test. 186 children not
exposed to cocaine had a mean score of 8.2 with a standard deviation of 3.0. Use
an alpha of 0.05 to test the claim that cocaine use is harmful to children’s aptitude
(Triola 2008).
107.
Use the following data (representing hospital admissions from motor vehicle
crashes) and an α-level of 0.05 to test the claim that Friday the 13ths are unlucky
(Triola 2008):
Friday the 6th
(immediately preceding the 13th)
9
6
11
11
3
5
Friday the 13th
13
12
14
10
4
12
108.
A study was conducted to investigate the
effectiveness of hypnotism in reducing
pain. Results for randomly selected
subjects are given below. The
measurements represent a pain scale
(where higher #’s indicate more pain). Use
an α-level of 0.05 to test the claim that
hypnosis lowers pain.
109.
To test the effectiveness of a drug to relieve asthma, a group of subjects was
randomly given a drug and placebo on two different occasions. After 1 hour an
asthmatic relief index was obtained for each subject, with these results:
Use 0.05 for an α-level. Is the drug effective (Hint: low numbers are good!)?
Subject
Drug
Placebo
1
28
32
2
31
33
3
17
19
4
22
26
5
12
17
Before Hypnosis
6.6
6.5
9.0
10.3
11.3
8.1
6.3
11.6
6
32
30
7
24
26
8
18
19
After Hypnosis
6.8
2.4
7.4
8.5
8.1
6.1
3.4
2.0
9
25
25
110. Here is a table showing who survived the sinking of the Titanic based on whether
they were crew members or passengers booked in first, second or third-class staterooms:
Crew First Second Third Total
203
118
178
711
Alive 212
122
167
528
1490
Dead 673
325
285
706
2201
Total 885
Determine if surviving was independent of cabin status (use alpha=0.01).
111. Use the following data to do a test of independence to see if left-handedness is
independent of gender (use an α-level of 0.05):
Male
Female
112.
Left-Handed
17
16
Right-Handed
83
184
Use the data at the right to do a
test of independence to see if
height is independent of gender
(use an α-level of 0.05):
Male
Female
Short
3
17
Tall
25
2
113.
A die is filled with a lead weight and then rolled 200 times with the following
results:
Result
1
2
3
4
5
6
Number of 27
31
42
40
28
32
times
Use an α-level of 0.05 to test the claim that the outcomes are not equally likely
(Triola 2008).
114.
The following data lists automobile fatalities by day of week:
Sun
Mon
Tue
Wed
Thu
Fri
Sat
132
98
95
98
105
133
158
Use an α-level of 0.05 to test the claim that the outcomes are not uniformly spread
across the days of the week (Triola 2008).
115.
The following data lists the birth months of Oscar-winning actors:
Jan
Feb Mar Apr May Jun Jul
Aug Sep Oct Nov Dec
9
5
7
14
8
1
7
6
4
5
1
9
Use an α-level of 0.05 to test the claim that the outcomes are not uniformly spread
across the months (Triola 2008).
116.
You are planning to open an old time soda fountain and your partner claims that
the public will not prefer any flavor over another. The flavors you serve are
cherry, strawberry, orange, lime and grape. After several customers, you stop and
take a look at how sales are going and here are the results. The following numbers
of people ordered the flavor shown. Cherry 35, Strawberry 32, Orange 29, Lime
26 and Grape 25. Test to see if there was a preference at the 0.05 significance
level.