Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 2.5, Problem 25E
A single car is randomly selected from among all of those registered at a local tag agency. What do you think of the following claim? “All cars are either Volkswagens or they are not. Therefore, the
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Calculate the 90% confidence interval for the population mean difference using the data in the attached image. I need to see where I went wrong.
Microsoft Excel snapshot for random sampling: Also note the formula used for the last
column
02
x✓ fx =INDEX(5852:58551, RANK(C2, $C$2:$C$51))
A
B
1
No.
States
2
1
ALABAMA
Rand No.
0.925957526
3
2
ALASKA
0.372999976
4
3
ARIZONA
0.941323044
5
4 ARKANSAS
0.071266381
Random Sample
CALIFORNIA
NORTH CAROLINA
ARKANSAS
WASHINGTON
G7
Microsoft Excel snapshot for systematic sampling:
xfx INDEX(SD52:50551, F7)
A
B
E
F
G
1
No.
States
Rand No. Random Sample
population
50
2
1 ALABAMA
0.5296685 NEW HAMPSHIRE
sample
10
3
2 ALASKA
0.4493186 OKLAHOMA
k
5
4
3 ARIZONA
0.707914 KANSAS
5
4 ARKANSAS 0.4831379 NORTH DAKOTA
6
5 CALIFORNIA 0.7277162 INDIANA
Random Sample
Sample Name
7
6 COLORADO 0.5865002 MISSISSIPPI
8
7:ONNECTICU 0.7640596 ILLINOIS
9
8 DELAWARE 0.5783029 MISSOURI
525
10
15
INDIANA
MARYLAND
COLORADO
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...
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- Suppose the Internal Revenue Service reported that the mean tax refund for the year 2022 was $3401. Assume the standard deviation is $82.5 and that the amounts refunded follow a normal probability distribution. Solve the following three parts? (For the answer to question 14, 15, and 16, start with making a bell curve. Identify on the bell curve where is mean, X, and area(s) to be determined. 1.What percent of the refunds are more than $3,500? 2. What percent of the refunds are more than $3500 but less than $3579? 3. What percent of the refunds are more than $3325 but less than $3579?arrow_forwardA normal distribution has a mean of 50 and a standard deviation of 4. Solve the following three parts? 1. Compute the probability of a value between 44.0 and 55.0. (The question requires finding probability value between 44 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 44, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the answer of the second part.) 2. Compute the probability of a value greater than 55.0. Use the same formula, x=55 and subtract the answer from 1. 3. Compute the probability of a value between 52.0 and 55.0. (The question requires finding probability value between 52 and 55. Solve it in 3 steps. In the first step, use the above formula and x = 52, calculate probability value. In the second step repeat the first step with the only difference that x=55. In the third step, subtract the answer of the first part from the…arrow_forwardIf a uniform distribution is defined over the interval from 6 to 10, then answer the followings: What is the mean of this uniform distribution? Show that the probability of any value between 6 and 10 is equal to 1.0 Find the probability of a value more than 7. Find the probability of a value between 7 and 9. The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be: More than $27? Less than or equal to $24? The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches. What is the mean amount of rainfall for the month? What is the probability of less than an inch of rain for the month? What is the probability of exactly 1.00 inch of rain? What is the probability of more than 1.50 inches of rain for the month? The best way to solve this problem is begin by a step by step creating a chart. Clearly mark the range, identifying the…arrow_forward
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