ACSI
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A researcher selects every 641th social security number and surveys the corresponding person.
Systematic sampling
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. A woman experienced a tax audit. The tax department claimed that the woman was audited because every 7500th person on the taxpayer list was being audited.
Systematic sampling
A presidential candidate plans to begin her campaign by visiting the capitals in 3 of 45 states. What is the probability that she selects the route of three specific capitals?
45 P 3 = 85140 1/85140
Which of the following is NOT a principle of probability? A.The probability of an impossible event is 0. B. All events are equally likely in any probability procedure. C. The probability of any event is between 0 and 1 inclusive. D. The probability of an event that is certain to occur is 1.
All events are equally likely in any probability procedure.
Events that are _______ cannot occur at the same time
disjoint
The classical approach to probability requires that the outcomes are _______.
equally likely.
The _______ for a procedure consists of all possible simple events or all outcomes that cannot be broken down any further.
sample space
Winning the jackpot in a particular lottery requires that you select the correct four numbers between 1 and 63 and, in a separate drawing, you must also select the correct single number between 1 and 31. Find the probability of winning the jackpot.
(1/(63 C 4)) * (1/(31 C 1)) 1/18465615
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed below are the phenotype codes where 1=smooth-yellow, 2=smooth-green, 3=wrinkled-yellow, and 4=wrinkled-green. Do the results make sense? 2 2 2 2 1 3 1 2 3 2 3 1 4 1
(a) 2.1 (b) 2 (c) 2 (d) 2.5 (e) Only the mode makes sense since the data is nominal.
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the weights in pounds of 11 players randomly selected from the roster of a championship sports team. Are the results likely to be representative of all players in that sport's league? 245 268 272 275 186 292 221 198 186 262 262
(a) 242.5 (b) 262 (c) 186 and 262 (d) 239 (e) The results are not likely to be representative because the championship team may not be representative of the entire league
In an experiment, college students were given either four quarters or a $1 bill and they could either keep the money or spend it on gum. The results are summarized in the table. Complete parts 1 through 3 below. Students Given Four Quarters Purchased Gum - 26 Kept the Money - 13 Students Given a $1 Bill Purchased Gum - 18 Kept the Money - 29 1. Find the probability of randomly selecting a student who spent the money, given that the student was given four quarters. 2. Find the probability of randomly selecting a student who kept the money, given that the student was given four quarters. 3. What do the preceding results suggest? a) A student given four quarters is more likely to have kept the money. b) A student given four quarters is more likely to have kept the money than a student given a $1 bill. c) A student given four quarters is more likely to have spent the money than a student given a $1 bill. d) A student given four quarters is more likely to have spent the money.
(a) 26(num purchased)/39(num with quarters) =0.667 (b)13/39 = 0.333 (c)A student given four quarters is more likely to have spent the money.
A thief steals an ATM card and must randomly guess the correct five-digit pin code from a 5-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
(a) 5^5 = 3125 (b) 1/3125
A study conducted at a certain college shows that 65% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 11 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to three decimal places as needed.
.65^11 = 0.009
It is impossible to get 7 kings when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
0
Refer to the sample data for pre-employment drug screening shown below. If one of the subjects is randomly selected, what is the probability that the test result is a false positive? Who would suffer from a false positive result? Why? Pre-Employment Drug Screening ResultsPositive test resultNegative test result Drug Use Is IndicatedDrug Use Is Not IndicatedSubject Uses Drugs 46 9 Subject Is Not a Drug User 2 30
0.023 The person tested would suffer because he or she would be suspected of using drugs when in reality he or she does not use drugs.
In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 202 answered "none," 296 said "one," 373 said "two," 151 said "three," and 72 responded with four or more. A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05.
0.066 No, because the probability of a respondent with four or more cell phones in use is greater than 0.05.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 317 272 239 140 Order Not Accurate 40 52 39 17 If one order is selected, find the probability of getting an order that is not accurate.
0.113
Sixteen of the 100 digital video recorders(DVRs) in an inventory are known to be defective. What is the probability that a randomly selected item isdefective?
0.16
In a test of a gender-selection technique, results consisted of 207 baby girls and 204 baby boys. Based on this result, what is the probability of a girl born to a couple using this technique? Does it appear that the technique is effective in increasing the likelihood that a baby will be a girl?
0.504 No
In a certain country, the true probability of a baby being a boy is 0.536. Among the next four randomly selected births in the country, what is the probability that at least one of them is a girl?
0.536^4 = 0.0825 1-0.0825 = 0.917
The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency table below summarizes the results. If we randomly select one of the customers represented in the table, what is the probability that the waiting time is at least 12 minutes or between 8 and 15 minutes? Round to three decimal places as needed. Waiting Time (minutes) Number of Customers 0-3 9 4-7 10 8-11 12 12-15 4 16-19 4 20-23 2 24-27 2
0.558
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 323 262 242 129 Order Not Accurate 36 51 38 19 If one order is selected, find the probability of getting food that is not from Restaurant A.
0.674
You are certain to get a red card when selecting 27 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
1
A research center poll showed that 82% of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief?
1-0.82= 0.18
If you know the names of the remaining seven students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?
1/5040 (5040 found from 7!)
The accompanying table shows the results from a test for a certain disease. Find the probability of selecting a subject with a negative test result, given that the subject has the disease. What would be an unfavorable consequence of this error? yes no positive 329 6 Negative 10 1174
10(number with disease and neg)/ 339(number who had the disease) = 0.029 The subject would not receive treatment and could spread the disease.
How many ways can you make change for a quarter? (Different arrangements of the same coins are not counted separately.)
12
In a small private school, 6 students are randomly selected from 16 available students. What is the probability that they are the six youngest students?
16 C 6 = 8008 1/8008
The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability (in fractional form) that the person is over 40 and drinks cola. Cola Root beer Lemon-lime Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35
20/225 = 4/51
Which of the following values cannot be probabilities? 0.03, 2^1/2, −0.47, 1.23, 3/5, 0, 5/3,
2^1/2 5/3 1.23 -0.47 any value less than 1 or greater than 1
Find the probability that when a couple has two children, at least one of them is a boy. (Assume that boys and girls are equally likely.)
3/4 bb bg gb gg
The table below shows the soft drinks preferences of people in three age groups. If one of the 255 subjects is randomly selected, find the probability that the person drinks root beer given that they are over 40. Cola Root Beer Lemon-lime Under 21 years of age 40 25 20 Between 21 and 40 35 20 30 Over 40 years of age 20 30 35
30(number of over 40 drinking rootbeer)/ 85(number over 40) = 6/17
In the game of blackjack played with one deck, a player is initially dealt 2 different cards from the 52 different cards in the deck. A winning "blackjack" hand is won by getting 1 of the 4 aces and 1 of 16 other cards worth 10 points. The two cards can be in any order. Find the probability of being dealt a blackjack hand. What approximate percentage of hands are winning blackjack hands?
32/663 4.83%
If a person is randomly selected, find the probability that his or her birthday is not in May. Ignore leap years.
334/365
A classic counting problem is to determine the number of different ways that the letters of "magically" can be arranged. Find that number
9!(number of letters)/2!2!(Letters repeated) = 90720
Refer to the table which summarizes the results of testing for a certain disease. A test subject is randomly selected and tested for the disease. What is the probability the subject has the disease given that the test result is negative. Round to three decimal places as needed. Positive Test Result Negative Test Result Subject has the disease 87 9 Subject does not have the disease 27 312
9/(312+9)= 0.028
Mean in Excel
=AVERAGE(number 1, [number 2], ...)
Median in Excel
=MEDIAN(number 1, [number 2], ...)
Mode in Excel
=MODE(...) Only can find one mode
Determine whether the value given below is from a discrete or continuous data set. In an election poll, Chris received 16,923,770 votes.
A discrete data set because there are a finite number of possible values.
Which word is associated with multiplication when computing probabilities?
AND
Which of the following would NOT cast doubt of the usefulness of sample data?
An effective sampling method
When 100 engines are shipped, all of them are free of defects. Select a written description of the complement of the given event.
At least one of the engines is defective.
In horse racing, a trifecta is a bet that the first three finishers in a race are selected, and they are selected in the correct order. Does a trifecta involve combinations or permutations? Explain.
Because the order of the first three finishers does make a difference, the trifecta involves permutations.
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. To determine customer opinion of their safety features, Daimler−Chrysler randomly selects 80 service centers during a certain week and surveys all customers visiting the service centers.
Cluster
Identify which type of sampling is used: random, systematic, convenience, stratified, or cluster. An internet site asks its members to call in their opinion regarding their reluctance to provide cresdit info online
Convenience
Which of the following is associated with a parameter?
Data that were obtained from an entire population.
Determine whether the given description corresponds to an observational study or an experiment. In a study of 437 girls with a particular disease, the subjects were photographed daily.
Does the given description correspond to an observational study or an experiment? The given description corresponds to an observational study.
Determine whether the results below appear to have statistical significance, and also determine whether the results have practical significance. In a study of a weight loss program, 7 subjects lost an average of 49 lbs. It is found that there is about a 33% chance of getting such results with a diet that has no effect.
Does the weight loss program have statistical significance? No, the program is not statistically significant because the results are likely to occur by chance. Does the weight loss program have practical significance? Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.
If A denotes some event, what does A denote? If P(A)=0.993, what is the value of P(A)?
Event A denotes the complement of event A, meaning that A consists of all outcomes in which event A does not occur. If P(A)=0.993, what is the value of P(A)? P(A)=0.007
An ad for a device used to discourage laptop thefts stated that "This device reduces your odds of laptop theft by 400 percent." What is wrong with thisstatement?
If the device eliminated all laptop thefts, it would reduce the odds of laptop theft by 100%, so 400% figure is misleading
Which of the following would be considered practically significant?
In a very large study, it was found that Treatment I resulted in 93% success while Treatment II resulted in 75% success.
Survey questions may be misleading if they are "loaded." To what does "loaded" refer?
Intentionally worded to elicit a desired response
Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 540 human resource professionals, each was asked about the importance of the education of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm
It appears to be sound because the data are not biased in any way.
When randomly selecting an adult, let B represent the event of randomly selecting someone with type B blood. Write a sentence describing what the rule of complements below is telling us. P(B or line overB)=1
It is certain that the selected adult has type B blood or does not have type B blood.
Determine whether the sampling method described below appears to be sound or is flawed. In a survey of 766 subjects, each was asked how often he or she ate bananas. The survey subjects were internet users who responded to a question that was posted on a news website.
It is flawed because it is a voluntary response sample.
The IQ score and brain volume are listed for each of five different subjects. Refer to the table of measurements below. Given that the data are matched and considering the units of the data, does it make sense to use the difference between each IQ score and brain volume that is in the same column? Why or why not?
No, it does not make sense to use the difference between each IQ score and brain volume in the same column, because IQ scores and brain volumes use different units of measurement.
When randomly selecting an adult, A denotes the event of selecting someone with blue eyes. What do P(A) and PA represent?
P(A) represents the probability of selecting an adult with blue eyes. PA represents the probability of selecting an adult who does not have blue eyes.
In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D)=0.750, where D is directly in person. If someone is randomly selected, what does PD represent, and what is its value?
PD is the probability of randomly selecting someone who does not choose a directin-person encounter as the most fun way to flirt. 1-0.75=0.25
Which of the following is NOT a voluntary response sample?
Quiz scores from a college level statistics course are analyzed to determine student progress.
Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. A large company wants to administer a satisfaction survey to its current customers. Using their customer database, the company randomly selects 30 customers and asks them about their level of satisfaction with the company.
Random
Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. In a poll conducted by a certain research center, 1160 adults were called after their telephone numbers were randomly generated by a computer, and 73% were able to correctly identify the
Random sampling
Selections made with replacement are considered to be _______.
Selections made with replacement are considered to be independent.
Determine whether the underlined number is a statistic or a parameter. A sample of employees is selected and it is found that 40% own a vehicle
Statistic because the value is a numerical measurement describing a characteristic of a sample
When testing a new treatment, what is the difference between statistical significance and practical significance? Can a treatment have statistical significance, but not practical significance?
Statistical significance is achieved when the result is very unlikely to occur by chance. Practical significance is related to whether common sense suggests that the treatment makes enough of a difference to justify its use. It is possible for a treatment to have statistical significance, but not practical significance.
Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster. To determine her breathing rate, Charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her breathing rate at 3 randomly selected times during each part of the day.
Stratified
Identify the type of sampling used: random, systematic, convenience, stratified, or cluster. To estimate the percentage of defects in a recent manufacturing batch, a quality control manager at General Foods selects every 17th soup can that comes off the assembly line starting with the ninth until she obtains a sample of 50 soup cans.
Systymatic
In a state pick 4 lottery game, a bettor selects four numbers between 0 and 9 and any selected number can be used more than once. Winning the top prize requires that the selected numbers match those and are drawn in the same order. Do the calculations for this lottery involve the combinations rule or either of the two permutations rules? Why or why not? If not, what rule does apply?
The combination and permutations rules do not apply because repetition is allowed and numbers are selected with replacement. The multiplication counting rule applies to this problem.
State whether the data described below are discrete or continuous, and explain why. The weights of dogs (in pounds) at a dog show
The data are continuous because the data can take on any value in an interval.
State whether the data described below are discrete or continuous, and explain why. the times required by students to complete a statistics test
The data are continuous because the data can take on any value in an interval.
State whether the data described below are discrete or continuous, and explain why. the number of children in families
The data are discrete because the data can only take on specific values.
Determine whether the data described below are qualitative or quantitative and explain why. The marital status of survey subjects
The data are qualitative because they don't measure or count anything
Refer to the sample of body temperatures (degrees Fahrenheit) in the table below. Given these temperatures, what issue can be addressed by conducting a statistical analysis of the data?
The data can be used to address the issue of whether there is a correlation between body temperatures at 8 AM and at 12 AM.
Determine whether the given value is a statistic or a parameter. A homeowner measured the voltage supplied to his home on all 30 days of a given month, and the average (mean) value is 127.1 volts.
The given value is a parameter for the month because the data collected represent a population.
In a study designed to test the effectiveness of a medication as a treatment for lower back pain, 1643 patients were randomly assigned to one of three groups: (1) the 547 subjects in the placebo group were given pills containing no medication; (2) 550 subjects were in a group given pills with the medication taken at regular intervals; (3) 546 subjects were in a group given pills with the medication to be taken when needed for pain relief. In what specific way was replication applied in the study?
The group sample sizes are all large so the researchers could see the effects of the treatment.
What does it mean for the findings of a statistical analysis of data to be statistically significant?
The likelihood of getting these results by chance is very small.
Assume that 1900 births are randomly selected and 1818 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
The number of girls is significantly high.
Assume that 1800 births are randomly selected and 64 of the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither significantly low nor significantly high.
The number of girls is significantly low.
Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.
The probability is 0.344 10^49^4=343910^4= 10000 3439/10000=0.344
What does P(B|A) represent?
The probability of event B occurring after it is assumed that event A has already occurred
Let event A=subject is telling the truth and event B=polygraph test indicates that the subject is lying. Use your own words to translate the notation P(B|A) into a verbal statement.
The probability that the polygraph indicates lying given that the subject is actually telling the truth.
There are 15,958,866 adults in a region. If a polling organization randomly selects 1235 adults without replacement, are the selections independent or dependent? If the selections are dependent, can they be treated as independent for the purposes of calculations?
The selections are dependent, because the selection is done without replacement. Yes, because the sample size is less than 5% of the population.
In a double-blind experiment designed to test the effectiveness of a new medication as a treatment for lower back pain, 1643 patients were randomly assigned to one of three groups: (1) the 547 subjects in the placebo group were given pills containing no medication; (2) 550 subjects were in a group given pills with the new medication taken at regular intervals; (3) 546 subjects were in a group given pills with the new medication to be taken when needed for pain relief. What does it mean to say that the experiment was "double-blind"?
The subjects in the study did not know whether they were taking a placebo or the new medication, and those who administered the pills also did not know.
A magazine, which does not accept free products or advertising from anyone, prints a review of new cars. Are there sources of bias in this situation?
There do not appear to be any sources of bias.
Determine whether the source given below has the potential to create a bias in a statistical study. A certain medical organization tends to oppose the use of meat and dairy products in our diets, and that organization has received hundreds of thousands of dollars in funding from an animal rights foundation.
There does appear to be a potential to create a bias. There is an incentive to produce results that are in line with the organization's creed and that of its funders.
Determine whether the source given below has the potential to create a bias in a statistical study. Washington University obtained word counts from the most popular novels of the past five years.
There does not appear to be a potential to create a bias. The organization would not gain from putting a spin on the results.
What is the goal of learning statistics?
To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed
Two events A and B are _______ if the occurrence of one does not affect the probability of the occurrence of the other.
Two events A and B are independent if the occurrence of one does not affect the probability of the occurrence of the other.
Which of the following is NOT a misuse of statistics?
Utilizing valid statistical methods and correct sampling techniques
A polling company reported that 49% of 1018 surveyed adults said that secondhand smoke is "quite annoying." Complete parts (a) through (d) below.
What is the exact value that is 49% of 1018 498.82 Could the result from part (a) be the actual number of adults who said that secondhand smoke is "quite annoying"? Why or why not? No, the result from part (a) could not be the actual number of adults who said that secondhand smoke is "quite annoying" because a count of people must result in a whole number. What could be the actual number of adults who said that secondhand smoke is "quite annoying" 499 Among the 1018 respondents, 417 said that secondhand smoke is "not at all annoying." What percentage of respondents said that secondhand smoke is "not at all annoying" 40.96%
The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 16.8% daily failure rate. Complete parts (a) through (d) below.
What is the probability that the student's alarm clock will not work on the morning of an important final exam? 0.1680.168 (Round to three decimal places as needed.) Part 2 b. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam? 0.028220.02822 (Round to five decimal places as needed.) Part 3 c. What is the probability of not being awakened if the student uses three independent alarm clocks? 0.004740.00474 (Round to five decimal places as needed.) Part 4 d. Do the second and third alarm clocks result in greatly improved reliability? A. Yes, because total malfunction would not be impossible, but it would be unlikely.
Refer to the table of body temperatures (degrees Fahrenheit). Is there some meaningful way in which each body temperature recorded at 8 AM is matched with the 12 AM temperature?
Yes. Each column of 8 AM and 12 AM temperatures is recorded from the same subject, so each pair is matched.
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 317 269 234 131 Order Not Accurate 30 55 38 11 If two orders are selected, find the probability that they are both from Restaurant D. a. Assume that the selections are made with replacement. Are the events independent? b. Assume that the selections are made without replacement. Are the events independent?
a. Assume that the selections are made with replacement. Are the events independent? The probability of getting two orders from Restaurant D is 0.01710.0171. The events are independent because choosing the first order does not affect the probability of the choice of the second order. (Do not round until the final answer. Round to four decimal places as needed.) Part 2 b. Assume that the selections are made without replacement. Are the events independent? The probability of getting two orders from Restaurant D is 0.01700.0170. The events are not independent because choosing the first order affects the probability of the choice of the second order. (Do not round until the final answer. Round to four decimal places as needed.)
Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table. Drive-thru Restaurant A B C D Order Accurate 337 271 238 135 Order Not Accurate 32 57 34 17 If one order is selected, find the probability of getting an order from Restaurant A or an order that is accurate. Are the events of selecting an order from Restaurant A and selecting an accurate order disjoint events?
accurate 0.904 The events are not disjoint because it is possible to receive an accurate order from Restaurant A.
Determine whether the description corresponds to an observational study or an experiment. Forty patients with skin cancer are divided into two groups. One group receives an experimental drug to fight cancer, the other a placebo. After two years, the spread of cancer is measerd
experiment
If you drew one card from a standard deck, would it be "significant" to draw a 5? Answer the question, considering an event to be "significant" if its probability is less than or equal to 0.05.
no
As a procedure is repeated again and again, the relative frequency of an event tends to approach the actual probability. This is known as _______.
the law of large numbers.
Complete the following statement. P(A or B) indicates _______.
the probability that in a single trial, event A occurs, event B occurs, or they both occur.
Are the events disjoint? Event 1: Get a full-time day job as a teller with a bank. Event 2: Get a full-time day job as a cashier at a store.
yes