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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Briefly explain the relationship between inferential statistics and sampling.
Suppose a town consists of 2,000 people, 1,100 of whom are registered voters.You are interested in how the people in this town will vote on a bond issue.What group constitutes the population? Give an
What is sampling error? Give an example. Is there any way to eliminate sampling error?
What is non sampling error? Give an example. Is there any way to eliminatenon sampling error?
State whether each of the following represents sampling or non sampling error.(a) The sample weight of newborn babies is taken with a scale that is inaccurateby 1 lb.(b) Sample data suggest that the
What is a representative sample? Why is getting a representative sampleimportant?
Briefly explain the relationship between sampling cost and sampling error.Give some examples of sampling costs.
The mean life of light bulbs produced by the Brite Lite Bulb Company is 950 hwith a standard deviation of 225 h. Assume that the population is normallydistributed. Suppose you take a random sample of
Suppose the mean amount of money spent by students on textbooks each semester is $175 with a standard deviation of $25. Assume that the population is normally distributed. Suppose you take a random
The Better Health Cereal Company produces Healthy Oats cereal. The true mean weight of a box of cereal is 24 oz with a standard deviation of 1 oz. Assume the population is normally distributed.
Explain the relationship between a probability distribution and a sampling distribution.
Suppose the average time a customer waits at the check-out line in a grocerystore is 12 min with a standard deviation of 3 min. If you take a random sampleof five customers, what is the probability
Historically, 65 % of the basketball players from Slam Dunk University graduate in 4 years. If a random sample of 50 former players is taken, what proportion of the samples is likely to have at least
A coffee machine is set so that it dispenses a normally distributed amount of coffee with a mean of 6 oz and a standard deviation of .4 oz. Samples of 12 cups of coffee are taken. What is the
Suppose that historically 61 % of the companies on the NYSE have prices that go up each year. If random samples of 100 stocks are taken, what proportion of samples is likely to have between 55 % and
Suppose the mean life for a company’s batteries is 12 h with a standard deviation of 3 h. If you take a sample of 20 batteries, what is the standard deviation of the sampling distribution of the
The mean useful life of better traction tires is 40,000 miles with a standard deviation of 4,000 miles. If you purchase four of these tires for your car, what is the probability that the mean useful
The professor in a statistics course takes a random sample of 100 students from campus to determine the number in favor of multiple-choice tests. Suppose that 50 % of the entire college population
Suppose 40 % of the students in Genius High School scored above 650 on the math portion of the SAT. What is the probability that more than 50 % of a random sample of 150 students will score less than
The Sorry Charlie Tuna Company produces canned tuna fish. The true mean weight of a can of tuna is 6 oz with a standard deviation of 1 oz. Assume the population is normally distributed, and suppose
Suppose the time a customer waits in line at a bank averages 8 min with a standard deviation of 2 min. In a random sample of five customers, what is the probability that the average time in line will
In Freeport High School, 40 % of the seniors who are eligible to vote indicated that they plan to vote in the upcoming election. What is the probability of selecting a random sample of 400 students
A credit card company accepts 70%of all applicants for credit cards. A random sample of 100 applications is taken.(a) What is the probability that the sample proportion of acceptance is between .60
From past history, a bookstore manager knows that 25 % of all customers entering the store make a purchase. Suppose 200 people enter the store.(a) What is the mean of the sample proportion of
Suppose 60 % of the members in a lifeguards’ union favor certification tests for lifeguards. If a random sample of 100 lifeguards is taken, what is probability that the sample proportion in favor
A bank knows that its demand deposits are normally distributed with a mean of $1,122 and a standard deviation of $393. A random sample of 100 deposits is taken.(a) What is the probability that the
A company claims that its accounts receivable follow a normal distribution with a mean of $500 and a standard deviation of $75. An auditor will certify the bank’s claim only if the mean of a random
Consider the members of a group with ages 23, 19, 25, 32, and 27. If a random sample of two is to be taken without replacement, what is the sampling distribution for their mean age? What is the mean
Consider a population of six numbers, 1, 2, 3, 4, 5, and 6. What is the mean of this population? Suppose you roll a pair of dice. Construct a table showing the different possible combinations of the
Compute the values for if N n
Why are we interested in the sample mean and its distribution?
Consider the members of a weight-loss group who weigh 225, 231, 195, 184, and 131 lb. If a simple random sample of size 2 is to be taken without replacement, what is the sampling distribution for
Suppose there are 2,000 members in a construction workers’ union and 40 % of the members favor ratifying the union contract. If a random sample of 100 construction workers is taken, what is the
From past history, a service manager at Honest Abe’s Auto Dealership knows that 35 % of all customers entering the dealership will have service work done that is under warranty. Suppose 200 people
A quality control engineer knows from past experience that the mean weight for ball bearings is 7.4 oz with a standard deviation of 1.2 oz. Suppose the engineer draws a random sample of 20 ball
Suppose you take an ordinary deck of 52 cards randomly select five cards without replacement. How many different combinations of sample car can you have?
Suppose you draw three balls without replacement from a bag of balls numbered 1–10. How many different possible combinations sample balls you have?
Suppose the ages of members of a senior citizens’ bridge club are 63, 71, 82, 60, 84, 75, 77, 65, and 70.(a) Compute the population mean and standard deviation for the age of the bridge club
In each of the following cases, find the mean a standard deviation of the sampling distribution for the sample mean, for a sample of size n from a population with mean m and standard deviation σ.
Suppose the cost of sampling is 50 cents per observation. If the population has zero variance, large a sample should be collected to estimate mean of the population?
Suppose you would like to randomly select four of the following six companies for a study: IBM, Apple Computer, AT&T, MCI, Ford, and Chrysler. What is the probability that Apple Computer will be in
Suppose a population is normally distributed. What is the probability that the sample mean will be less than the population mean?
Suppose an obstetrician knows from past experience that the mean weight of a newborn baby is 7.5 lb with a standard deviation of 2 lb. The doctor randomly chooses five newborn babies. What is the
Use the information given in question 7 to find P(X ≤ 8).Question 7Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability that the variable will
Use the information given in question 7 to find P(X < 2 or X > 10).Question 7Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability that the variable
Draw the cumulative distribution function for the distribution given in question 7.Question 7Suppose a random variable X can take on only values in the range from 2 to 10 and that the probability
Suppose a random variable X is best described by a uniform distribution with a = 8 and b = 20.(a) Find f(x).(b) Find F(x).(c) Find the mean and variance of X.
Suppose a random variable Y is best described by a uniform distribution with a = 3 and b = 32.(a) Find f(y).(b) Find F(y).(c) Find the mean and variance of Y.
A very observant art thief (who should probably be teaching statistics instead) notices that the frequency of security guards passing by a museum is uniformly distributed between 15 and 60 min.
Use the information given in question 14.(a) Find the probability that the guard passes by within 35 min of the thief’s arrival.(b) Find the probability that the guard does not pass by within 30
An art dealer at an auction believes that the bid on a certain painting will be a uniformly distributed random variable between $500 and $2,000.(a) What is the probability density function for this
Suppose X has an exponential distribution with λ = 5. Find the following probabilities: (a) P(X (b) P(X > 4) > .7) (c) P(X > .50) V V V
Suppose X has an exponential distribution with λ = 4. Find the following probabilities: VI VI VI (a) P(X .3) (b) P(X < .5) (c) P(X 1.6)
Suppose X has an exponential distribution with λ = 1/3 . Find the following probabilities: (a) P(3 < X < 5) (b) P(5 X 10) (c) P(2 < X < 1)
Suppose the random variable X is best approximated by an exponential distribution with λ = 8. Find the mean and the variance of X.
Suppose the random variable Y is best approximated by an exponential distribution with λ = 3. Find the mean and the variance of Y.
Find tα for the following: (a) = .05 and v = 10 x (b)x= .025 and v = 4 (c) = .10 and v = 7
Find the value t0 such that to) = .025, where v = 6 .05, where v 12 .10, where v = 9 (a) P(t (b) P(t to) = (c) P(t to) =
Find the value t0 such that (a) P(t to) =.10, where v = 25 (b) P(t to) = .025, where v = 14 (c) P(t to) = .01, where v = 17
Find the following probabilities for the t distributions. (a) P(t> 3.078) (b) P(t < 1.943) (c) P(t > 2.492) if v = 1 if v = 6 if v = 24
Find the following probabilities for the t distributions. (a) P(t > 1.734) if y = 18 (b) P(t > 1.943) if v = 6 (c) P(t < 1.645) if v =
Find the following values. ,2 a.
Find the following values. 2 NI a.
Find the following probabilities. (a) P(x > 10.8564) (b) P( 59.1963) when v = 24 when v = 24 when v = 70 when v = 90
Find the following probabilities. (a) P(x < 3.84146) when v = 1 (b) P(Z P 15.9871) when v = 10 (c) P(x 140.169) when v= 100 (d) P(x > 1.61031) when v = 5
Find the following Fν1;ν2;α values. (a) v = 8, V = 10, and x = .01 (b) v = 3, V = 11, and x = .005 (c) v = 12, v2 = 9, and x = .05 (d) v = 24, v2 = 19, and x = .025 vi V2
Find the following Fν1;ν2;α values. (a) v = 10, V2 = 10, and = .05 Vi (b) v = 15, v = (c) v = 12, v = V2 (d) v = 20, V2 = 3, and x = .01 15, and x = .025 10, and x = .005
Find the probabilities, given v1 and v2 as shown. (a) v = 1 and v = 3; P(F> 17.44) (b) v = 3 and v = 1; P(F > 864.2)
Using the MINITAB program, find the probabilities, given v1 and v2 as shown. (a) v = 120 and v = 120; P(F > 1.35) (b) v = 00 and v = o; P(F > 1.00) 0; (c) v = 6 and v2 = 17; P(F < 3.28) (d) v = 3 and
Find the probability that an exponentially distributed random variable X with mean 1/λ = 8 will take on the values:(a) Between 2 and 7(b) Less than 9(c) Greater than 6(d) Between 1 and 15
Suppose the lifetime of a television picture tube is distributed exponentially with a standard deviation of 1,400 h. Find the probability that the tube will last:(a) More than 3,000 h(b) Less than
Suppose the time you wait at a bank is exponentially distributed with mean 1/λ = 12 min. What is the probability that you will wait between 10 and 20 min?
Suppose the length of time people wait at a fast-food restaurant is distributed exponentially with a mean of 1/7 min. Use MINITAB to answer the following questions.(a) What percentage of people will
Suppose the length of time a student waits to register for courses is distributed exponentially with a mean of 1/15 min.(a) What percentage of students will register within 10 min?(b) What percentage
Suppose a random variable is distributed as an x2 distribution with n degrees of freedom. Consider the probability P(x2 ≤ 9). Explain the relationship between the probability and the degrees of
Suppose a random variable is distributed as Student’s t distribution with (n - 1) degrees of freedom. Consider the probability P(t ≥ .7). Explain the relationship between the probability and the
The incomes of families in a town are assumed to be uniformly distributed between $15,000 and $85,000. What is the probability that a randomly selected family will have an income above $40,000?
At an antiques auction, the winning bids were found to be uniformly distributed between $500 and $2,500. What is the probability that a winning bid was less than $1,000? What is the probability that
The manager of a department store notices that the amount of time a customer must wait before being helped is distributed uniformly between 1 and 4 min.Find the mean and variance of the time a
A quality control expert for the Healthy Time Cereal Company notices that in a 16-oz package of cereal, the amount in the box is uniformly distributed between 15.3 and 17.1 oz. Find the mean and
The shelf life of hearing aid batteries is found to be approximated by an exponential distribution with a mean of 1/12 day. What fraction of the batteries would be expected to have a shelf life
A computer programmer has decided to use the exponential distribution to evaluate the reliability of a computer program. After 10 programming errors were found, the time (measured in days) to find
An advertising executive believes that the length of time a television viewer can recall a commercial is distributed exponentially with a mean of .25 days.Find how long it will take for 75 % of the
An investment advisor believes that the rate of return for Horizon Company’s stock is uniformly distributed between 3 % and 12 %. Find the probability that the return will be greater than 5 %. Find
The mean life of a computer’s hard disk is found to be exponentially distributed with a mean of 12,000 h. Find the proportion of hard disks that will have a life greater than 20,000 h.
Suppose the life of a car battery is assumed to be uniformly distributed between 3.9 and 7.3 years. Find the mean and variance of the life of a car battery.
The chief financial officer at Venture Corporation believes that an investment in a new project will have a cash flow in year one that is uniformly distributed between $1 million and $10 million.
The campus bus at Haverford College is scheduled to arrive at the business school at 8:00 a.m. Usually, the bus arrives at the bus stop during the interval 7:56–8:03. Assume that the arrival time
A gas station’s owner found that about two cars come into the station every minute. If the arrival time follows an exponential distribution, what is the probability that the next car will arrive in
A college professor gives a standardized test to her students every semester.She finds that the students’ grades follow a uniform distribution with 100 points as the maximum and 65 points as the
Briefly explain how the mean, standard deviation, coefficient of variation, and skewness can be used to analyze the returns of IBM and Boeing in Table 9.1.Table 9.1 Company name 1 3M Co. 2 Alcoa Inc.
Suppose the weight of a football team is uniformly distributed with a minimum weight of 175 lb and a maximum weight of 285 lb.(a) Find the mean weight of the team.(b) Compute the standard deviation
A bank manager finds that about six customers enter the bank every 5 min. If the customer arrival time follows an exponential distribution, what is the probability that the next customer will arrive
Suppose the life of a steel-belted radial tire is uniformly distributed between 30,000 and 45,000 miles.(a) Find the mean tire life.(b) Find the standard deviation of tire life.(c) What percentage of
Briefly discuss the relationship among and F distributions. 2 t, X
Given v1 = 5 and a = .05, find v2 for the following F values.(a) 5.05(b) 3.33(c) 2.53
In their study, Vardeman and Ray found that the number of accidents per hour at an industrial plant is exponentially distributed with a mean λ = .5. Use the formula f(t) = λe - λt to determine
Suppose there is a sample of 30 items drawn from a normal population. Find the probability that the sample variance exceeds 36.6869.
Suppose there are two independent normal populations with population variances o = 4.5 and o2 = 2.5, respectively. Two random samples of sizes s and s2, respectively, are drawn from the two normal
A random sample of size 7 is drawn from a population with population variance σ2 = 2.5.(a) Determine the probability that the variance of the sample is greater than 7.008.(b) Determine the

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