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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Use the data from question 27 and your results from question 28 to estimate the number of accidents for each trucker. Also calculate the errors from the regression line.Question 27Suppose you are a
Suppose a labor economist at the Department of Labor estimates the following relationship between years of experience and earnings of accountants. Earnings = 22,000+ 3,200(years of experience)
Now suppose the actual earnings of the 5 accountants in question 30 are as follows. Calculate the error from the regression.Question 30Suppose a labor economist at the Department of Labor estimates
In order to determine whether a company should encourage its employees to live close to work, an efficiency expert collects data on the number of latenesses per month and the number of miles an
The manager of the Tow Time Auto Club would like to know the relationship between the age of a car and the number of service calls per year. He collects the following information:(a) Draw a scatter
Explain what we mean by the goodness of fit for a regression. Give two measures we can use to assess the goodness of fit.
Use the results from question 33 to predict the number of service calls for a car that is 3 years old and for one that is 6 years old.Question 33The manager of the Tow Time Auto Club would like to
Suppose you have the following information about number of dollars spent on advertising, X, and amount of car sales, Y: Cov(X,Y) = 500, Var(X) = 250, Var(Y) = 1,000, mean of X = 1,000, and mean of Y
Use the information given in question 36 to find the correlation between advertising dollars and sales.Question 36Suppose you have the following information about number of dollars spent on
Briefly define total deviation, unexplained deviation, and explained deviation.
Use the data and results from question 21 to calculate SSE, SSR, SST, and the coefficient of determination. Interpret what the coefficient tells us.Question 21You are given the following information
Suppose you collect data for IBM’s sales and dollars spent on advertising and then compute the following statistics:(a) Compute the correlation coefficient between advertising dollars and sales.(b)
A grocery store sells an average of 478 loaves of bread each week. Sales (X) are normally distributed with a standard deviation of 17.(a) If a random sample of size n = 1 (week) is drawn, what is the
A random variable s measures the daily balances in customers’ savings accounts. It is normally distributed, with a mean of μs – $108 and a standard deviation of $15.(a) If a random sample of
On average, a book distributor fills orders for 1,000 books per day. If daily orders are normally distributed and the standard deviation is 100, what is the probability that a 5-day average will be
A company makes a pastry called a chocco. During the manufacturing process, the individual choccos are placed in a baking oven. The time it takes to bake them is normally distributed around a mean of
In a large group of corporate executives, 20 % have no college education, 10 % have exactly 2 years of college, 20 % have exactly 4 years, and 50 % have 6 years. A sample size of 2 (with replacement)
Out of 10 pay telephones located in a municipal building, two phones are to bepicked at random, with replacement, for a study of phone use. The actual usageof the phones on a particular day is shown
To demonstrate the central limit theorem, draw 100 samples of size 5 from a random-number table and calculate the sample mean for each of the 100 samples. Construct a frequency distribution of sample
The accompanying probability density function is a uniform distributionshowing that a certain delicate new medical device will fail between 0 and10 years after it is implanted in the human body. The
The daily catch of a small tuna-fishing fleet averages 130 t. The fleet’s logbook shows that the weight of the catch varies from day to day and this variation is measured by the standard deviation
A type of cathode ray tube has a mean life of 10,000 h and a variance of 3,600. If we take samples of 25 tubes each and for each sample we find the mean life, between what limits (symmetric with
The population of times measured by 3-min egg timers is normally distributed with μ = 3 min and σ = .2 min. We test samples of 25 timers. Find the time that would be exceeded by 95 % of the sample
A light bulb manufacturer claims that 90 % of the bulbs it produces meet tough new standards imposed by the consumer protection agency. You just received a shipment containing 400 bulbs from this
At the beginning of every decade, the US government conducts a census. Why does it take a census? What are the advantages of a census over a sample?
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

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