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mathematics
business statistics

Questions and Answers of Business Statistics

Consider the following sample of five chemical yields:a. Use this sample to test H0: Md = 800 versus Ha: Md ‰ 800 by setting Î± = .01.b. Use this sample to test H0: Md = 750
A local newspaper randomly selects 20 patrons of the Springwood Restaurant on a given Saturday night and has each patron rate the quality of his or her meal as 5 (excellent), 4 (good), 3 (average), 2
Explain the circumstances in which we use the Wilcoxon rank sum test.
Identify the parametric test corresponding to the Wilcoxon rank sum test. What assumption is needed for the validity of this parametric test (and not needed for the Wilcoxon rank sum test)?
A loan officer at a bank wishes to compare the new car loan rates charged at banks in Ohio with the new car loan rates of Ohio credit unions. Two independent random samples of bank rates and credit
Explain the circumstances in which we use the Wilcoxon signed ranks test.
Identify the parametric test corresponding to the Wilcoxon signed ranks test. What assumption is needed for the validity of the parametric test (and not needed for the Wilcoxon signed ranks test)?
Explain the circumstances in which we use the Kruskal–Wallis H test.
Identify the parametric test corresponding to the Kruskal–Wallis H test.
What are the assumptions needed for the validity of the parametric test identified in Exercise 17.21 that are not needed for the Kruskal–Wallis H test?Exercise 17.21Identify the parametric test
Use the Kruskal€“Wallis H test to compare display panels A, B, and C using the data in Table 17.8. Use Î± = .05.Table 17.8Use the given independent samples to perform the
Use the Kruskal€“Wallis H test to compare bottle designs A, B, and C using the data in Table 17.9. Use Î± = .01.Table 17.Use the given independent samples to perform the
Use the Kruskal€“Wallis H test and the Minitab output in Figure 17.5 to compare the bottom (B), middle (M), and top (T) display heights using the data in Table 17.10. Use Î± =
Explain the circumstances in which we use Spearman’s rank correlation coefficient.
A drug company wishes to compare the effects of three different drugs (X, Y, and Z) that are being developed to reduce cholesterol levels. Each drug is administered to six patients at the recommended
Table 17.16 gives the median 2009 and 2010 prices for used homes (in thousands of dollars) for six randomly selected U.S. housing markets. Use a nonparametric test to attempt to show that housing
During 2011 a company implemented a number of policies aimed at reducing the ages of its customers€™ accounts. In order to assess the effectiveness of these measures, the company randomly
Explain the differences between(a) Decision making under certainty,(b) Decision making under uncertainty,(c) Decision making under risk.
Explain how to use the(a) Maximin criterion,(b) Maximax criterion,(c) Expected monetary value criterion.
Explain how to find the expected value of perfect information.
Find the best alternative (and the resulting payoff) in the given payoff table if it is known with certainty that demand will bea. Low.b Medium.c High.The example involves a capacity-planning problem
Given the payoff table, find the alternative that would be chosen using the maximin criterion.The example involves a capacity-planning problem in which a company must choose to build a small, medium,
Given the payoff table, find the alternative that would be chosen using the maximax criterion.The example involves a capacity-planning problem in which a company must choose to build a small, medium,
Suppose that the company assigns prior probabilities of .3, .5, and .2 to low, moderate, and high demands, respectively.a. Find the expected monetary value for each alternative (small, medium, and
Construct a decision tree for the information in the payoff table assuming that the prior probabilities of low, moderate, and high demands are, respectively, .3, .5, and .2.The example involves a
For the information in the payoff table finda. The expected payoff under certainty.b. The expected value of perfect information, EVPI.The example involves a capacity-planning problem in which a
A firm wishes to choose the location for a new factory. Profits obtained will depend on whether a new railroad spur is constructed to serve the town in which the new factory will be located. The
Construct a decision tree for the information given in Exercises 18.10 and 18.11.Exercise 18.10 and Exercise 18.11 No New Railroad Spur New Railroad Alternatives Spur Built $1* $14 Location A
Refer to the information given in Exercise 18.10. Using the probabilities of .60 for a new railroad spur and .40 for no new railroad spur.a. Compute the expected monetary value for each location.b.
Figure 18.3 gives a decision tree presented in the book Production/Operations Management by William J. Stevenson. Use this tree diagram to do the following:a. Find the expected monetary value for
Identify and list each of the following for the investor€™s decision problem:a. The investor€™s alternative actions.b. The states of nature.c. The possible results of sampling
Carry out a prior analysis of the investor€™s decision problem. That is, determine the investment choice that should be made and find the expected monetary value of that choice assuming
Carry out a posterior analysis of the investor€™s decision problem. That is, determine the investment choice that should be made and find the expected monetary value of that choice
Carry out a preposterior analysis of the investor€™s decision problem by finding:a. The expected monetary value associated with consulting the economist; that is, find the EPS.b. The
Identify and list each of the following for the control device situation:a. The firm’s alternative actions.b. The states of nature.c. The possible results of sampling (that is, of information
Construct a decision tree for a prior analysis of the control device situation. Then determine whether the engineers should be sent, assuming that the piece of test equipment is not employed to check
Set up probability revision tables to:a. Find the probability that the test equipment “reads in,” and find the posterior probabilities of in alignment and out of alignment given that the test
Carry out a posterior analysis of the control device problem. That is, decide whether the engineers should be sent, and find the expected monetary value associated with either sending or not sending
What is a utility?
Carry out a preposterior analysis of the control device problem by finding:a. The expected monetary value associated with using the test equipment; that is, find the EPS.b. The expected monetary
Suppose that a decision maker has the opportunity to invest in an oil well drilling operation that has a .3 chance of yielding a profit of $1,000,000, a .4 chance of yielding a profit of $400,000,
Consider Exercise 18.31. Find the expected utility of the oil well drilling operation. Find the expected utility of not investing. What should the decision maker do if he/she wishes to maximize
Write out the payoff table for the investor€™s decision problem.An Introduction to Decision Analysis, 2nd ed., Robert T. Clemen presents an example in which an investor wishes to choose
In the book Making Hard Decisions: An Introduction to Decision Analysis, Robert T. Clemen presents a decision tree for a research and development decision (note that payoffs are given in millions of
In the book Production/Operations Management, William J. Stevenson presents a decision tree concerning a firm€™s decision about the size of a production facility. This decision tree is
Consider the decision tree in Figure 18.9 and the situation described in Exercise 18.34. Suppose that a marketing research study can be done to obtain more information about whether demand will be
Discuss the purpose of differencing.
Explain how we use the SAC and SPAC.
Use Excel, MegaStat, or Minitab to perform a regression analysis of the Bonner Frozen Foods sales volume data in Table 14.5 on page 599 by using the model y = Î²0+ Î²1x1+
How do we model the interaction between two independent variables?
When does a scatter plot suggest the use of the quadratic regression model?
What is a qualitative independent variable?
Consider a hospital for which XRay = 56,194, BedDays = 14,077.88, and LengthStay = 6.89. A 95 percent prediction interval for the labor hours corresponding to this combination of values of the
Use the Bonner Frozen Foods sales volume data in Table 14.5 on page 599 and the model y = β0 + β1x1 + β2x2 + ε to find(1) A point estimate of and a 95 percent confidence interval for the mean
What is the purpose of the overall F test?
What is estimated by the mean square error, and what is estimated by the standard error?
When developing a regression model to predict a dependent variable y, it is best, if there are enough data, to €œbuild€ the model using one data set (called the training data
How do we check the normality assumption?
Explain what is meant by the population correlation coefficient ρ.
Use the real estate sales price data in Table 13.7 to find(1) A point estimate of and a 95 percent confidence interval for the mean sales price of all houses having a size of 20 (that is, 2,000
Use the sales volume data in Figure 3.22(a) to find (1) A point estimate of and a 95 percent confidence interval for the mean sales volume in all sales regions when advertising expenditure is 10
What does the simple coefficient of determination measure?
What is estimated by the mean square error, and what is estimated by the standard error?
What is the purpose behind summarizing data in the form of a two-way contingency table?
Consider the sample of 100 waiting times given in Table 1.9. Use these data to carry out a chi-square goodness-of-fit test to determine whether the population of all waiting times is normally
Consider the sample of 60 bottle design ratings given in Table 1.6. Use these data to carry out a chi-square goodness-of-fit test to determine whether the population of all bottle design ratings is
In an article in the Accounting Review, Brown and Solomon study the effects of two factors€”confirmation of accounts receivable and verification of sales transactions€”on account
What is a treatment in the context of a two-factor factorial experiment?
How can we test to determine if the blocks we have chosen are reasonable?
In your own words, explain why we sometimes employ the randomized block design.
Explain the assumptions that must be satisfied in order to validly use the one-way ANOVA formulas.
Suppose a company wishes to compare the hourly output of its employees before and after vacations. Explain how you would collect data for a paired difference experiment to make this comparison.
Why is a paired difference experiment sometimes more informative than an independent samples experiment? Give an example of a situation in which a paired difference experiment might be advantageous.
Explain how a paired difference experiment differs from an independent samples experiment in terms of how the data for these experiments are collected.
What assumption must hold to make statistical inferences about a population variance?
What condition must be satisfied in order for the methods of this section to be appropriate?
If we wish to test a hypothesis to provide evidence supporting the claim that fewer than 5 percent of the units produced by a process are defective, formulate the null and alternative hypotheses.
Explain what a p-value is, and explain how it is used to test a hypothesis.
Define a population total. Give an example of a population total that a business might estimate.
Discuss when it is appropriate to use the t-based confidence interval for μ.
For a fixed level of confidence, what happens to a confidence interval for μ when we increase the sample size?
For a fixed sample size, what happens to a confidence interval for μ when we increase the level of confidence?
Explain the meaning of the term “95 percent confidence.”
Describe the effect of increasing the sample size on the population of all possible sample proportions.
If the sample size n is large, the sampling distribution of p̂ is approximately a normal distribution. What condition must be satisfied to guarantee that n is large enough to say that p̂ is
The sampling distribution of p̂ is the probability distribution of a population. Describe this population.
What does the Central Limit Theorem tell us about the sampling distribution of the sample mean?
The sampling distribution of the sample mean x̅ is the probability distribution of a population. Describe this population.
If a normal probability plot has the appearance of a straight line, what should we conclude?
Explain the relationship between the Poisson and exponential distributions.
Under what condition may we use the normal approximation to the binomial distribution?
Explain why it might be convenient to approximate binomial probabilities by using areas under an appropriate normal curve.
Explain how to compute the z value corresponding to a value of a normally distributed random variable. What does the z value tell us about the value of the random variable?
What two properties must be satisfied by a continuous probability distribution (or probability curve)?
How do we use the continuous probability distribution (or probability curve) of a random variable x to find probabilities? Explain.
A discrete probability distribution assigns probabilities to individual values. To what are probabilities assigned by a continuous probability distribution?
Explain the meaning of a positive covariance.
Explain the meaning of a negative covariance.
In the context of the hypergeometric distribution, explain the meanings of N, r, and n.
Explain the logic behind the rare event approach to making statistical inferences.

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