Questions and Answers of Statistical Techniques in Business

For Exercises 45 through 50, use the following price information for selected items for 2015 and 2022. Production figures for those two periods are also given.Determine a value index for 2022 using
Refer to the Baseball 2021 data, which report information on the 30 Major League Baseball teams for the 2021 season. Consider the following variables: number of wins, payroll, season attendance,
Sun Ray Candles has several retail stores in the coastal areas of North and South Carolina. Many of their customers ask the store to ship their purchases. The following chart shows the number of
Aki Zhang owns and manages an investment portfolio of 36 stocks. Listed here is the holding time (recorded to the nearest whole year) between purchase and sale for the collection of 36
According to PMQ Pizza Magazine (https://www.pizzatoday.com/pizzeria-rankings/ 2019-top-100-pizza-companies/), an estimate of pizza sales in the United States for the top 100 pizza companies was
In 2020, the United States exported a total of $256.2 billion worth of products to Canada (https://www.trade.gov/knowledge-product/canada-market-overview). The top five categories relative to dollar
In the United States, agriculture is big business. For the period 2020–2021, agriculture accounted for nearly 20% of gross domestic product. Farming is the main driver of the industry. In 2020,
Compute the mean of the following population values: 14, 10, 14, 6, 14, 8.
Bouchard and Associates specialize in corporate law. They charge $100 an hour for researching a case, $75 an hour for consultations, and $200 an hour for writing a brief. Last week one of the
You have funds invested in a mutual fund of S&P 500 stocks. Over the last 5 years, the annual percent returns of the S&P 500 are 19.42%, − 6.24%, 28.88%, 16.26%, and 14.49%. What is the
You currently have $10,000 invested. If your goal is to increase this investment to $1,000,000 in 30 years, what annual percent growth rate would be needed?
Goodcarbadcar is an online portal (www.goodcarbadcar.net) that reports automotive industry data. The table shows the number of cars sold in the United States in 2019 and 2020. The top 34 brands are
For each U.S. state and the District of Columbia, the following table lists the total employees and number of total employees represented by unions.Use statistical software to answer the following
In 2021, 188 women played the Ladies Professional Golf Association (LPGA) tour. A random sample of 30 players is selected and their winnings recorded. The sample is listed here.a. Determine the
Trea Turner of the Los Angeles Dodgers had the highest batting average for the 2021 Major League Baseball season. His average was .328. So, the likelihood of his getting a hit is .328 for each time
(a) Evaluate(b) Evaluate 1.24e-2²/2 dz.
Find a recursion formula forin terms of (k+1)
Find P(A ∩ B) if P(A) = 0.2, P(B) = 0.4, and P(A|B) + P(B|A) = 0.75.
An urn contains six chips numbered 1 through 6. Three are drawn out. What outcomes are in the event “Second smallest chip is a 3”? Assume that the order of the chips is irrelevant.
A restaurant offers a choice of four appetizers, fourteen entrees, six desserts, and five beverages. How many different meals are possible if a diner intends to order only three courses? (Consider
Consider the experiment of choosing coefficients for the quadratic equation ax2 + bx + c = 0. Characterize the values of a, b, and c associated with the event A: Equation has complex roots.
How many ways can a set of four tires be put on a car if all the tires are interchangeable? How many ways are possible if two of the four are snow tires?
A poker player is dealt a 7 of diamonds, a queen of diamonds, a queen of hearts, a queen of clubs, and an ace of hearts. He discards the 7. What is his probability of drawing to either a full house
A new horror movie, Friday the 13th, Part X, will star Jason’s great-grandson (also named Jason) as a psychotic trying to dispatch (as gruesomely as possible) eight camp counselors, four men and
What must be true of events A and B if(a) A ∪ B = B(b) A ∩ B = A
Let events A and B and sample space S be defined as the following intervals:S = {x : 0 ≤ x ≤ 10}A = {x : 0 < x < 5}B = {x : 3 ≤ x ≤ 7}Characterize the following events:(a) AC(b) A ∩
In how many ways can a pack of fifty-two cards be dealt to thirteen players, four to each, so that every player has one card of each suit?
A computer is instructed to generate a random sequence using the digits 0 through 9; repetitions are permissible. What is the shortest length the sequence can be and still have at least a 70%
Ten equally qualified marketing assistants are candidates for promotion to associate buyer; seven are men and three are women. If the company intends to promote four of the ten at random, what
A chemical engineer wishes to observe the effects of temperature, pressure, and catalyst concentration on the yield resulting from a certain reaction. If she intends to include two different
A coded message from a CIA operative to his Russian KGB counterpart is to be sent in the form Q4ET, where the first and last entries must be consonants; the second, an integer 1 through 9; and the
Express the following probabilities in terms of P(A), P(B), and P(A ∩ B).(a) P(AC ∪ BC)(b) P(AC ∩ (A ∪ B))
If P(A|B) < P(A), show that P(B|A) < P(B).
Given that P(A) = a and P(B) = b, show that P(A/B) ≥ a+b-1 b
How many terms will be included in the expansion of(a + b + c)(d + e + f )(x + y + u + v + w)Which of the following will be included in that number: aeu, cdx, bef, xvw?
A committee of fifty politicians is to be chosen from among our one hundred U.S. senators. If the selection is done at random, what is the probability that each state will be represented?
A fast-food restaurant offers customers a choice of eight toppings that can be added to a hamburger. How many different hamburgers can be ordered?
Suppose that n fair dice are rolled. What are the chances that all n faces will be the same?
Let P be the set of right triangles with a 5'' hypotenuse and whose height and length are a and b, respectively. Characterize the outcomes in P.
Suppose a baseball player steps to the plate with the intention of trying to “coax” a base on balls by never swinging at a pitch. The umpire, of course, will necessarily call each pitch either a
Does a monkey have a better chance of rearrangingACCLLU U S to spell CALCU LU SorAABEGLR to spell ALGEBRA?
In international Morse code, each letter in the alphabet is symbolized by a series of dots and dashes: the letter a, for example, is encoded as “· –”. What is the minimum number of dots and/or
Given that P(A ∩ BC) = 0.3, P((A ∪ B)C) = 0.2, and P(A ∩ B) = 0.1, find P(A|B).
Monica’s vacation plans require that she fly from Nashville to Chicago to Seattle to Anchorage. According to her travel agent, there are three available flights from Nashville to Chicago, five from
Given that P(A) + P(B) = 0.9, P(A|B) = 0.5, and P(B|A) = 0.4, find P(A).
The board of a large corporation has six members willing to be nominated for office. How many different “president/vice president/treasurer” slates could be submitted to the stockholders?
Find A ∩ B ∩ C if A = {x: 0 ≤ x ≤ 4}, B = {x: 2 ≤ x ≤ 6}, and C = {x: x = 0, 1, 2, . . .}.
The nine members of the music faculty baseball team, the Mahler Maulers, are all incompetent, and each can play any position equally poorly. In how many different ways can the Maulers take the field?
Nine cards are dealt from a 52-card deck. Write a formula for the probability that three of the five even numerical denominations are represented twice, one of the three face cards appears twice, and
Let A be the set of five-card hands dealt from a fifty-two-card poker deck, where the denominations of the five cards are all consecutive—for example, (7 of hearts, 8 of spades, 9 of spades, 10 of
A coke hand in bridge is one where none of the thirteen cards is an ace or is higher than a 9. What is the probability of being dealt such a hand?
A pinochle deck has forty-eight cards, two of each of six denominations (9, J, Q, K, 10, A) and the usual four suits. Among the many hands that count for meld is a roundhouse, which occurs when a
A coin is tossed four times and the resulting sequence of heads and/or tails is recorded. Define the events A,B, and C as follows:A: exactly two heads appearB: heads and tails alternateC: first two
If the definition of n! is to hold for all nonnegative integers n, show that it follows that 0! must equal 1.
The crew of Apollo 17 consisted of a pilot, a copilot, and a geologist. Suppose that NASA had actually trained nine aviators and four geologists as candidates for the flight. How many different crews
Stanley’s statistics seminar is graded on a Pass/Fail basis. At the end of the semester each student is given the option of taking either a two-question exam (Final A) or a three-question exam
What is the smallest number of switches wired in parallel that will give a probability of at least 0.98 that a circuit will be completed? Assume that each switch operates independently and will
In an upstate congressional race, the incumbent Republican (R) is running against a field of three Democrats (D1, D2, and D3) seeking the nomination. Political pundits estimate that the probabilities
Which state name can generate more permutations, TENNESSEE or FLORIDA?
Let A and B be any two events defined on a sample space S. Which of the following sets are necessarily subsets of which other sets?A B A∪B A∩B AC ∩ BA ∩ BC (AC ∪ BC)C
An interior decorator is trying to arrange a shelf containing eight books, three with red covers, three with blue covers, and two with brown covers.(a) Assuming the titles and the sizes of the books
Suppose a pitcher faces a batter who never swings. For how many different ball/strike sequences will the batter be called out on the fifth pitch?
Prove thatdirectly without appealing to any combinatorial arguments. n+1 (" + ¹) = ( 2 ) + (k²1) k
What is the coefficient of w2x3yz3 in the expansion of (w + x + y + z)9?
An automobile insurance company has compiled the information summarized below on its policy-holders. Suppose someone calls to file a claim. To which age group does he or she most likely belong? Age
Make an anagram out of the familiar expression STATISTICS IS FUN. In how many ways can the letters in the anagram be permuted?
How many straight lines can be drawn between five points (A, B, C, D, and E), no three of which are collinear?
The Alpha Beta Zeta sorority is trying to fill a pledge class of nine new members during fall rush. Among the twenty-five available candidates, fifteen have been judged marginally acceptable and ten
The final exam in History 101 consists of five essay questions that the professor chooses from a pool of seven that are given to the students a week in advance. For how many possible sets of
(a) Let 0 < a < b. Which number is larger?(b) Let a > 0. Which number is larger? b 2π -²/2 dz or -212 ² -2²12² dz -b. √2π
In how many ways can the letters in M I S S I S S I P P Ibe arranged so that no two I’s are adjacent?
If E(W) = μ and Var(W) = σ2, show that E = (W = ") = 0 = 0 and Var W-"). = 1
Hawaii’s fourteen-thousand-foot Mauna Loa is one of the world’s most active volcanoes. Between 1832 and 1950, it erupted thirty-seven times, which translates to a rate of 0.027 times per month.
In 2009 a donor who insisted on anonymity gave seven-figure donations to twelve universities. A media report of this generous but somewhat mysterious act identified that all of the universities
A certain hospitalization policy pays a cash benefit for up to five days in the hospital. It pays $250 per day for the first three days and $150 per day for the next two. The number of days of
For a high-risk driver, the time in days between the beginning of a year and an accident has an exponential pdf. Suppose an insurance company believes the probability that such a driver will be
Frankie and Johnny play the following game. Frankie selects a number at random from the interval [a, b]. Johnny, not knowing Frankie’s number, is to pick a second number from that same interval and
Suppose the charge for repairing an automobile averages $200 with a standard deviation of $16. If a 10% tax is added to the charge and then a $15 flat fee for environmental impact, what is the
Among the many letters sent to a popular advice to - the -lovelorn columnist, was one involving a paternity issue that raised an interesting statistical question. The distraught writer—call her
Use the method of maximum likelihood to estimate θ in the pdfEvaluate θe for the following random sample of size 4: y1 = 6.2, y2 = 7.0, y3 = 2.5, and y4 = 4.2. fy (y: 0) = 0 2√5 e √, y 20
The town of Willoughby has just been selected as the site for a new automobile assembly complex. City officials estimate that the anticipated influx of job-seeking families will add some four hundred
If the standard deviation (σ) associated with the pdf that produced the following sample is 3.6, would it be correct to claim thatis a 95% confidence interval for μ? Explain.
A random sample of size 8—x1 = 1, x2 = 0, x3 = 1, x4 = 1, x5 = 0, x6 = 1, x7 = 1, and x8 = 0—is taken from the probability function pX (k; θ) = θk(1 − θ)1−k, k = 0, 1; 0 < θ < 1Find
If ˆθ is sufficient for θ, show that any one-to-one function of ˆθ is also sufficient for θ.
Suppose that y1, y2, . . . , yn is a random sample of size n from a normal distribution where σ is known. Depending on how the tail-area probabilities are split up, an infinite number of random
Show that ˆσ2 =Σni=1 Y2i is sufficient for σ2 if Y1,Y2, . . . ,Yn is a random sample from a normal pdf with μ = 0.
What is the squared-error loss Bayes estimate for the parameter θ in a binomial pdf, where θ has a uniform distribution—that is, a noninformative prior? (Recall that a uniform prior is a beta pdf
For the negative binomial pdf pX (k; p, r) =find the maximum likelihood estimator for p if r is known. (k+r-11 (*+/-¹) (1 - p) ^ p², k
Let Y1,Y2, . . . ,Yn be a random sample of size n from the pdf fY (y; θ) = 1/(r − 1)!θr yr−1e−y/θ, y > 0(a) Show that ˆθ = 1/r y̅ is an unbiased estimator for θ.(b) Show that ˆθ =
Which of the following two intervals has the greater probability of containing the binomial parameter p? X n -0.67₁ (X/n)(1-X/n) n or X n +0.67₁ X n 8 (X/n)(1-X/n) n
During one of the first “beer wars” in the early 1980s, a taste test between Schlitz and Budweiser was the focus of a nationally broadcast TV commercial. One hundred people agreed to drink from
Use the method of moments to derive estimates for the parameters r and λ in the gamma pdf, fy (y; r, ) = T(r) les, y = 0
A criminologist is searching through FBI files to document the prevalence of a rare double-whorl fingerprint. Among six consecutive sets of 100,000 prints scanned by a computer, the numbers of
Given the massive amount of information available from the internet, public libraries might have little support. Yet, in a Pew Research Center poll of 6224 Americans age sixteen and over, 3921 said
A machine stamps out a certain type of automobile part. When working properly the part has an average weight of μ = 1.6 pounds and standard deviation σ = 0.22 pounds. To test the proper working of
How long does it take to fly from Atlanta to New York’s LaGuardia airport? There are many components of the time elapsed, but one of the more stable measurements is the actual in-air time. For a
Kepler’s third law states that “the squares of the periods of the planets are proportional to the cubes of their mean distance from the Sun.” Listed below are the periods of revolution (x), the
Given the pdf fY (y; θ) = 2y θ2 , 0 ≤ y ≤ θ. Take a sample of size 3 from this pdf. Use the statistic Ymax to test H0: θ = 5 versus H1: θ > 5. Recall that for n = 3 the pdf of Ymax is
Mandatory helmet laws for motorcycle riders remain a controversial issue. Some states have a “limited” ordinance that applies only to younger riders; others have a “comprehensive” statute
What “confidence” is associated with each of the following random intervals? Assume that the Yi’s are normally distributed.(a)(b)(c)(d) [Y- Y - 2.0930 S 20 °(5)] 20 Y + 2.0930

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