Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 2, Problem 149SE
A large group of people is to be checked for two common symptoms of a certain disease. It is thought that 20% of the people possess symptom A alone, 30% possess symptom B alone, 10%possess both symptoms, and the remainder have neither symptom. For one person chosen at random from this group, find these
- a The person has neither symptom.
- b The person has at least one symptom.
- c The person has both symptoms, given that he has symptom B.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
For the following questions (a - 1 ), assume that a population of frogs has an
average weight of = 23 grams and a
standard deviation (° ) equal to 1 gram.
You obtain a sample of N = 15 frogs,
where the average weight in grams (X)
equals 23.4 grams and s = 0.95. You wish
to conduct a hypothesis test specifying
Ho : 10 = 23 grams.
(a) Report the T-Score test statistic (T).
Round your answer to three decimal places.
(b) Based on the T-Score test statistic (T) in (a), do you have sufficient evidence to
reject Ho when a = 0.05 ?
(c) Based on the T-Score test statistic (T) in (a), do you make a Type I or Type Il error
when a = 0.05 ?
(d) Based on the T-Score test statistic (T) in (a), do you have sufficient evidence to
reject Ho when a = 0.01 ?
(e) Based on the T-Score test statistic (T) in (a), do you make a Type I or Type II error
when a = 0.01 ?
You obtain a sample of N = 15 frogs,
where the average weight in grams (X)
equals 23.4 grams and s = 0.95. You wish
to conduct a hypothesis test…
For the following questions (a - j), assume that a population of frogs has an average
weight of μ 23 grams and a standard deviation (σ) equal to 1 gram.
=
You obtain a sample of N = 15 frogs, where the average weight in grams (X) equals
23.4 grams and s = 0.95. You wish to conduct a hypothesis test specifying Ho: μo = 23
grams.
(a) Report the T-Score test statistic (T). Round your answer to three decimal places.
(b) Based on the T-Score test statistic (T) in (a), do you have sufficient evidence to
reject Ho when α = 0.05?
(c) Based on the T-Score test statistic (T) in (a), do you make a Type I or Type II er-
ror when α = 0.05?
(d) Based on the T-Score test statistic (T) in (a), do you have sufficient evidence to
reject Ho when a = 0.01?
(e) Based on the T-Score test statistic (T) in (a), do you make a Type I or Type II er-
ror when a = 0.01?
You obtain a sample of N = 15 frogs, where the average weight in grams (X) equals
23.4 grams and s = 0.95. You wish to conduct a hypothesis test…
This is statistics . I am really stuck. Please help!
Chapter 2 Solutions
Mathematical Statistics with Applications
Ch. 2.3 - Suppose a family contains two children of...Ch. 2.3 - Suppose that A and B are two events. Write...Ch. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Refer to Exercise 2.4. Use the identities...Ch. 2.3 - Suppose two dice are tossed and the numbers on the...Ch. 2.3 - A group of five applicants for a pair of identical...Ch. 2.3 - From a survey of 60 students attending a...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...Ch. 2.4 - The proportions of blood phenotypes. A, B, AB, and...
Ch. 2.4 - A sample space consists of five simple events. E1,...Ch. 2.4 - A vehicle arriving at an intersection can turn...Ch. 2.4 - Americans can be quite suspicious, especially when...Ch. 2.4 - A survey classified a large number of adults...Ch. 2.4 - An oil prospecting firm hits oil or gas on 10% of...Ch. 2.4 - Prob. 16ECh. 2.4 - Hydraulic landing assemblies coming from an...Ch. 2.4 - Suppose two balanced coins are tossed and the...Ch. 2.4 - A business office orders paper supplies from one...Ch. 2.4 - The following game was played on a popular...Ch. 2.4 - If A and B are events, use the result derived in...Ch. 2.4 - If A and B are events and B A, use the result...Ch. 2.4 - Prob. 23ECh. 2.4 - Use the result in Exercise 2.22 and the Axioms in...Ch. 2.5 - A single car is randomly selected from among all...Ch. 2.5 - According to Websters New Collegiate Dictionary, a...Ch. 2.5 - In Exercise 2.12 we considered a situation where...Ch. 2.5 - Four equally qualified people apply for two...Ch. 2.5 - Two additional jurors are needed to complete a...Ch. 2.5 - Three imported wines are to be ranked from lowest...Ch. 2.5 - A boxcar contains six complex electronic systems....Ch. 2.5 - A retailer sells only two styles of stereo...Ch. 2.5 - The Bureau of the Census reports that the median...Ch. 2.5 - Patients arriving at a hospital outpatient clinic...Ch. 2.6 - An airline has six flights from New York to...Ch. 2.6 - Prob. 36ECh. 2.6 - A businesswoman in Philadelphia is preparing an...Ch. 2.6 - An upscale restaurant offers a special fixe prix...Ch. 2.6 - An experiment consists of tossing a pair of dice....Ch. 2.6 - A brand of automobile comes in five different...Ch. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - A fleet of nine taxis is to be dispatched to three...Ch. 2.6 - Refer to Exercise 2.43. Assume that taxis are...Ch. 2.6 - Prob. 45ECh. 2.6 - Ten teams are playing in a basketball tournament....Ch. 2.6 - Refer to Exercise 2.46. If 2n teams are to be...Ch. 2.6 - Prob. 48ECh. 2.6 - Students attending the University of Florida can...Ch. 2.6 - Prob. 50ECh. 2.6 - A local fraternity is conducting a raffle where 50...Ch. 2.6 - An experimenter wishes to investigate the effect...Ch. 2.6 - Five firms, F1, F2,, F5, each offer bids on three...Ch. 2.6 - A group of three undergraduate and five graduate...Ch. 2.6 - A study is to be conducted in a hospital to...Ch. 2.6 - A student prepares for an exam by studying a list...Ch. 2.6 - Two cards are drawn from a standard 52-card...Ch. 2.6 - Five cards are dealt from a standard 52-card deck....Ch. 2.6 - Prob. 59ECh. 2.6 - Refer to Example 2.7. Suppose that we record the...Ch. 2.6 - Prob. 61ECh. 2.6 - A manufacturer has nine distinct motors in stock,...Ch. 2.6 - The eight-member Human Relations Advisory Board of...Ch. 2.6 - A balanced die is tossed six times, and the number...Ch. 2.6 - Prob. 65ECh. 2.6 - Refer to Example 2.10. What is the probability...Ch. 2.6 - Refer to Example 2.13. Suppose that the number of...Ch. 2.6 - Show that, for any integer n 1, a (nn)=1....Ch. 2.6 - Prob. 69ECh. 2.6 - Prob. 70ECh. 2.7 - If two events, A and B, are such that P(A) = .5,...Ch. 2.7 - For a certain population of employees, the...Ch. 2.7 - Gregor Mendel was a monk who, in 1865, suggested a...Ch. 2.7 - One hundred adults were interviewed in a telephone...Ch. 2.7 - Prob. 75ECh. 2.7 - A survey of consumers in a particular community...Ch. 2.7 - A study of the posttreatment behavior of a large...Ch. 2.7 - In the definition of the independence of two...Ch. 2.7 - Suppose that A and B are mutually exclusive...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If P(A) 0, P(B) 0, and P(A) P(A|B), show that...Ch. 2.7 - Suppose that A B and that P(A) 0 and P(B) 0....Ch. 2.7 - If A and B are mutually exclusive events and P(B) ...Ch. 2.8 - If A1, A2, and A3 are three events and...Ch. 2.8 - Prob. 85ECh. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Suppose that A and B are two events such that P(A)...Ch. 2.8 - Prob. 89ECh. 2.8 - Suppose that there is a 1 in 50 chance of injury...Ch. 2.8 - Can A an B be mutually exclusive if P(A) = .4 and...Ch. 2.8 - Prob. 92ECh. 2.8 - In a game, a participant is given three attempts...Ch. 2.8 - A smoke detector system uses two devices, A and B....Ch. 2.8 - Prob. 95ECh. 2.8 - If A and B are independent events with P(A) = .5...Ch. 2.8 - Consider the following portion of an electric...Ch. 2.8 - With relays operating as in Exercise 2.97, compare...Ch. 2.8 - Suppose that A and B are independent events such...Ch. 2.8 - Show that Theorem 2.6, the additive law of...Ch. 2.8 - Articles coming through an inspection line are...Ch. 2.8 - Diseases I and II are prevalent among people in a...Ch. 2.8 - Refer to Exercise 2.50. Hours after the rigging of...Ch. 2.8 - If A and B are two events, prove that...Ch. 2.8 - If the probability of injury on each individual...Ch. 2.8 - If A and B are equally likely events and we...Ch. 2.8 - Prob. 107ECh. 2.8 - If A, B, and C are three events, use two...Ch. 2.8 - Prob. 109ECh. 2.9 - Of the items produced daily by a factory, 40% come...Ch. 2.9 - Prob. 111ECh. 2.9 - Three radar sets, operating independently, are set...Ch. 2.9 - Consider one of the radar sets of Exercise 2.112....Ch. 2.9 - A lie detector will show a positive reading...Ch. 2.9 - Prob. 115ECh. 2.9 - A communications network has a built-in safeguard...Ch. 2.9 - A slate auto-inspection station has two inspection...Ch. 2.9 - Prob. 118ECh. 2.9 - Suppose that two balanced dice are tossed...Ch. 2.9 - Suppose that two defective refrigerators have been...Ch. 2.9 - Prob. 121ECh. 2.10 - Applet Exercise Use the applet Bayes Rule as a...Ch. 2.10 - Prob. 123ECh. 2.10 - A population of voters contains 40% Republicans...Ch. 2.10 - A diagnostic test for a disease is such that it...Ch. 2.10 - Prob. 126ECh. 2.10 - Prob. 127ECh. 2.10 - Use Theorem 2.8, the law of total probability, to...Ch. 2.10 - Males and females are observed to react...Ch. 2.10 - A study of Georgia residents suggests that those...Ch. 2.10 - Prob. 131ECh. 2.10 - A plane is missing and is presumed to have equal...Ch. 2.10 - A student answers a multiple-choice examination...Ch. 2.10 - Two methods, A and B, are available for teaching a...Ch. 2.10 - Of the travelers arriving at a small airport, 60%...Ch. 2.10 - Prob. 136ECh. 2.10 - Five identical bowls are labeled 1, 2, 3, 4, and...Ch. 2.10 - Prob. 138ECh. 2.11 - Refer to Exercise 2.112. Let the random variable Y...Ch. 2.11 - Refer to Exercise 2.120. Let the random variable Y...Ch. 2.11 - Refer again to Exercise 2.120. Let the random...Ch. 2.11 - A spinner can land in any of four positions, A, B,...Ch. 2 - Show that Theorem 2.7 holds for conditional...Ch. 2 - Let S contain four sample points, E1, E2, E3, and...Ch. 2 - Prob. 145SECh. 2 - Prob. 146SECh. 2 - Prob. 147SECh. 2 - A bin contains three components from supplier A,...Ch. 2 - A large group of people is to be checked for two...Ch. 2 - 2.149 A large group of people is to be checked for...Ch. 2 - Prob. 151SECh. 2 - Prob. 152SECh. 2 - Prob. 153SECh. 2 - a A drawer contains n = 5 different and...Ch. 2 - A group of men possesses the three characteristics...Ch. 2 - The accompanying table lists accidental deaths by...Ch. 2 - Prob. 157SECh. 2 - A bowl contains w white balls and b black balls....Ch. 2 - Prob. 159SECh. 2 - A machine for producing a new experimental...Ch. 2 - Prob. 161SECh. 2 - Prob. 162SECh. 2 - Relays used in the construction of electric...Ch. 2 - Prob. 164SECh. 2 - Refer to Exercise 2.163 and consider circuit B. If...Ch. 2 - Prob. 166SECh. 2 - Prob. 167SECh. 2 - As in Exercises 2.166 and 2.167, eight tires of...Ch. 2 - Three beer drinkers (say I, II, and III) are to...Ch. 2 - Prob. 170SECh. 2 - Prob. 171SECh. 2 - Prob. 172SECh. 2 - Prob. 173SECh. 2 - Prob. 174SECh. 2 - Prob. 175SECh. 2 - Prob. 176SECh. 2 - Refer to Exercise 2.90(b) where a friend claimed...Ch. 2 - Suppose that the probability of exposure to the...Ch. 2 - Two gamblers bet 1 each on the successive tosses...Ch. 2 - Prob. 180SECh. 2 - Suppose that n indistinguishable balls are to be...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Not use ai pleasearrow_forwardnot use ai pleasearrow_forwardThe term marketing mix refers to the different components that can be controlled in a marketing strategy to increase sales or profit. The name comes from a cooking-mix analogy used by Neil Borden in his 1953 presidential address to the American Marketing Association. In 1960, E. Jerome McCarthy proposed the “four Ps” of marketing—product, price, place (or distribution), and promotion—as the most basic components of the marketing mix. Variables related to the four Ps are called marketing mix variables. A market researcher for a major manufacturer of computer printers is constructing a multiple regression model to predict monthly sales of printers using various marketing mix variables. The model uses historical data for various printer models and will be used to forecast sales for a newly introduced printer. The dependent variable for the model is: y = sales in a given month (in thousands of dollars) The predictor variables for the model are chosen from the following marketing mix…arrow_forward
- 13. For the following studies, determine the null and alternative hypotheses and classify thehypothesis test as two tailed, left-tailed or right-tailed.a) A study was conducted comparing the wing lengths of two subspecies of dark-eyedjuncos. One of the subspecies migrates, the other does not. A hypothesis test is to beperformed to decide whether the mean wing length of the non-migratory birds is lessthan that of the migratory birds.b) A half-century ago, the average (U.S.) woman in her 20s was 62.6 inches tall. To see ifwoman tend to be taller, a random sample of 1000 women in their 20s was recentlyconducted and heights were recorded. A hypothesis test is to be performed to decide ifthe mean height of women in their 20s today is greater than that of the women in their20s a half-century ago.arrow_forward14. A study was done to test the relationship between breast milk and a child’s subsequentIQ. The researchers analyzed IQ data on 946 children at the age of 7 ½ to 8 years. Themothers of the children in the study had chosen whether to provide their infants withbreast milk. The researchers used the following designations. Group 1: mothersdeclined to provide breast milk; Group 2: mothers had chosen but were unable toprovide breast milk; Group 3: mothers had chosen and were able to provide breast milk.A hypothesis test is to be performed to decide if there is a difference in mean IQ amongthe three groups. Based on the methods studied in this class, what hypothesis test doyou think would fit the best? What would be the null hypothesis and what would be thealternative hypothesis? What are the assumptions for the test, and would you have anyconcerns about these assumptions.arrow_forward7. The National Center for Health Statistics conducts a National Health Interview Surveyevery year. Each year they randomly select U.S. households to interview. In 2020, theysurveyed 37,358 people and found that 3,624 of these people did not have healthinsurance. In 2021, they surveyed 37,989 people and found that 3,495 of these peopledid not have health insurance.At a 5% significance level, did the proportion of people who didn’t have healthinsurance decrease from 2020 to 2021?You need to use a hypothesis test for this, and you need to state your null andalternative hypotheses, your test statistic value, your p-value or critical value, and yourconclusion.arrow_forward
- 3. A woman wants to know what proportion of people in her town have health insurance.She comes up with three sampling ideas, described below. Discuss the pros and cons ofeach in terms of obtaining an unbiased, representative sample.a. She stands outside her local grocery store every evening for a week, from 5-7 pm, andasks every 10th person entering if they have health insurance.b. She throws ten darts at a map of the town and then tries her best to survey all thepeople who live in the houses closest to the darts.c. She posts a survey on her Facebook page and asks all her friends to share her survey.d. She pays for a small ad in the local newspaper in which she poses her question andprovides her email address and phone number and asks people to contact her to withtheir answer.arrow_forward5. A large, observational study once found that people who retired later in life tended tolive longer than those who retired early. The researchers concluded that people whowant to live longer should put off retirement until later in life. Do you agree with theirconclusion based on their study? Why or why not?arrow_forward11. Suppose a company claims that their lightbulb lasts an average of 5 years with astandard deviation of 0.5 years. (They are claiming that the population mean life of thebulb is 5 years with a population standard deviation of 0.5 years.) Assume theselightbulb lifetimes are normally distributed.a. Suppose you buy one light bulb and it only lasts you 4.5 years. Would you consider thatevidence against the company’s claim? (Hint: Assuming that the company’s claim istrue, determine the probability that a randomly selected bulb would last 4.5 years orless.)b. Suppose you buy 10 bulbs, and these 10 bulbs have a mean life of 4.5 years. Would youconsider that evidence against the company’s claim? (Hint: Assuming the company’sclaim is true, determine the probability that the mean of 10 randomly selected bulbswould last 4.5 years or less.)arrow_forward
- 6. It was reported in a news article that couples who combine finances are happier. Howwould you design an experiment to test a causal relationship?arrow_forwardConstruct a histogramof the scores, and then describe the distribution shape.71, 80, 92, 92, 61, 48, 62, 83, 87, 64, 96, 94, 89, 66, 57, 91, 52, 95, 53arrow_forward9. Suppose that from a random sample of 25 households that recently spent the day at anAmerican amusement park, the mean cost for the day was $220.00 with a samplestandard deviation of $30.00.a. Find a 90% confidence interval for the true mean cost of a day at an Americanamusement park.b. What assumptions did you make when constructing this interval?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Bayes' Theorem 1: Introduction and conditional probability; Author: Dr Nic's Maths and Stats;https://www.youtube.com/watch?v=lQVkXfJ-rpU;License: Standard YouTube License, CC-BY
What is Conditional Probability | Bayes Theorem | Conditional Probability Examples & Problems; Author: ACADGILD;https://www.youtube.com/watch?v=MxOny_1y2Q4;License: Standard YouTube License, CC-BY
Bayes' Theorem of Probability With Tree Diagrams & Venn Diagrams; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=OByl4RJxnKA;License: Standard YouTube License, CC-BY
Bayes' Theorem - The Simplest Case; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=XQoLVl31ZfQ;License: Standard Youtube License