Question: Some common applications of statistics in business

> The payoffs of a decision analysis problem are the payments to decision makers. 2. When it is uncertain which of the states of nature will occur and also the probability of each state of nature occurring is unknown, the scenario is referred to as decisio

> Reengineering is the approach to revise or redo the engineering design of a product in response to customer complaints.

> Chi-square goodness-of-fit tests are always one-tailed tests. 2. A chi-square goodness-of-fit test can be used as an alternative to z-test for population proportions if there are only two classifications. 3. A chi-square test of independence can be used

> In a one-way ANOVA the total variance is portioned into the variance due to treatments and the variance due to error. 2. A repeated measures design is a special case of the randomized block design.

> To test if the means of two populations are different, we test the significance of the difference between two sample means. 2. The distribution of the difference between two sample means may be considered to be normally distributed only if the two popula

> What is the relative frequency of type B in the previous question? a) 0.25 b) 0.35 c) 0.5 d) 0.64 29. In sciences and technology, use of pie charts is limited compared to other types of graphs such as a histogram, because __________. a) It is difficult

> A null hypothesis must always include the equality sign. 2. If the result of a hypothesis test is statistically significant, it must be considered a substantive result. 3. The null hypothesis is rejected if the p-value (i.e., the probability of getting a

> A statistic taken from a sample that is used to estimate a population parameter is called a point estimate. 2. An interval estimate is a range of values around the point estimate. 3. The width of the confidence interval does not depend on the desired le

> Systematic sampling is an example of random sampling which is often used because of its convenience and ease of administration. 2. Missing data and recording errors are examples of sampling error. 3. If a population is normal distributed, the means of th

> An exponential distribution, which is continuous, is closely related to the Poisson distribution, which is discrete.

> Binomial distribution applies only to experiments in which the trials are done with replacement or successive trials are independent. 2. A hypergeometric distribution is used in situations where the sampling is done from an infinite population and the s

> If two events with non-zero probabilities are mutually exclusive, they cannot be statistically independent. 2. The probability of the union of two events is always equal to the sum of the marginal probabilities of two independent events. 3. The joint pro

> An advantage of the median instead of using mean as the measure of central tendency is that it is not affected by extremely large or extremely small values in the data set. 2. The median and the second quartile of a data set are always equal. 3. Dependin

> Frequency distribution is a summary of data presented in the form of class intervals and frequencies. 2. Data that have been organized into a frequency distribution are called ungrouped data. 3. The sum of the frequencies of a grouped data set is always

> Virtually every area of business uses statistics in decision making. 2. The highest level of data measurement is the ratio-level measurement. 3. Since statistics deals with primarily with facts and figures, ethical considerations do not play any role in

> One strategy that can be used in making decisions under risk is the ___________. a) Expected monetary value approach b) Maximax risk criterion c) Minmax risk strategy d) Minimax regret strategy e) Maximax regret strategy 26. In a capacity expansion decis

> A histogram is vertical bar chart on an X-Y plane, in which the labels along horizontal (or X) axis represent the class end points and the bars along the vertical (or Y) axis show the ____. a) Class width b) Class range c) Class frequency d) Class mid-

> An approach to decision making under uncertainty that is based on a weighted combination of the maximum and the minimum payoffs from each alternative is called the _____________. a) Maximin criterion b) Maximax criterion c) Hurwicz criterion d) Minimax r

> The payoffs of a decision analysis problem are_______________________. a) The various choices or options available to the decision maker in any given problem situation. b) The occurrences of nature that can happen after a decision is made that can affect

> Consider two products, A and B. The quality of A is determined by the characteristic, its weight. The quality of B is determined by the characteristic, whether it is acceptable or not. Which of the following statements is true? a) Quality characteristics

> Many times in the implementation of quality improvement techniques, it is useful to explore the relationship between two numerical variables (e.g., the strength of steel bars and the carbon content of steel). A graphical mechanism to explore such relatio

> A major stumbling block to studying and implementing quality improvement methodologies is that __________. a) Quality is a hindrance to production b) Quality means different things to different people c) Customers care about price and not quality d) Prod

> Consider the data set in the table below, use the Wilcoxon Matched-Pairs Signed-Ranks Test to calculate the test statistic, and the test statistic is __________. a) 28 b) 24 c) 4 d) −24 22. The nonparametric alternative to the one-way

> In the Mann-Whitney U test using two large samples (i.e., size greater than 10), the decision to reject the null hypothesis that the two populations are identical versus the alternative hypothesis that they are not identical is taken by __________. a) Ca

> The administrator of a large university wants to test if students elected to a large student council were randomly selected from its two campuses, east (E) and west (W). A sequence of 26 consecutive students sampled showed the following pattern: E E E E

> The test used to analyze the frequencies of two variables with multiple categories to determine whether the two variables are independent is __________. a) The F-test b) The chi-square goodness-of-fit test c) The chi-square test of independence d) Binomi

> A business analyst wants to use the chi-square goodness-of-fit test if a uniform distribution is a good fit for the following observed frequencies in eight categories along a single dimension. The desired level of significance is 0.05. The correct decis

> Given a small dataset: 2.3, 7.1, 6.3, 5.8, 4.2, what is the range for this data? a) 1.9 b) 2.5 c) 4.8 d) 2.3 10. A useful tool for grouping data is __________. a) A frequency distribution b) Group dynamics c) Segmentation d) Constructive statistics 11

> A firm believes that the distribution of the economic class of its customers is 25%, 50%, and 25% in the three possible categories (i.e., lower income class, middle-income class, or upper income class). To test if this belief is true, data from a random

> A regression model, Monthly Sales = 750 + 0.20 (Month), was developed to predict the monthly sales (in $1,000s) using the data from the months, 1, 2, …, 12 of the past year. The forecast using this model for the first month of the next year will be _____

> A forecasting technique that is not appropriate for forecasting time-series data that are stationary is __________. a) A naïve forecasting model b) An averaging model c) A simple linear regression model d) An exponential model 12. The techniques used for

> Data gathered on any characteristic of interest (e.g., a company’s sales) over a period of time (e.g., past five or ten years) at regular intervals (e.g., a month or a quarter) is called time-series data. Which of the following elements

> If a data set contains 6 independent variables, the number of all possible regression models will be __________. a) 31 b) 62 c) 63 d) 64 22. The main difference between forward selection and stepwise regression is this: __________. a) Forward selection i

> Which of the following statements is true with regard to higher order (third. fourth, etc.) multiple regression models? a) They do not usually fit the data better than lower-order models. b) The R2 of higher-order models will generally be less than that

> If the scatter plot of y variable versus x variable shows a parabolic shape, which of the following steps would be appropriate to explore the relationship between the two variables? a) Add two more x variables to the regression model b) Add a log x varia

> In a regression study, a multiple regression model with two explanatory variables is developed using a data set with 23 observations. In the ANOVA table for this model, the sum of squares total (SSyy) is = 12500 and the sum of squares error (SSE) = 3000.

> In testing the overall significance of a multiple regression model, the null hypothesis that each one of the β-coefficients of the x-variables in the model is equal to zero, is tested against the alternative hypothesis that __________. a) Each one of the

> The graph of a regression equation with one independent variable, y = b0 + b1 x, yields a straight line in a two-dimensional (x, y) space. To graph a regression equation with two independent variables, y = b0 + b1 x1 + b2 x2, we require a 3-dimensional s

> Which of the following categories of business analytics builds and assesses algorithmic models aimed at making empirical rather than theoretical predictions and is designed to predict future observations: a) Descriptive analytics b) Predictive analytics

> The data in the table below represent number of months spent training (x) and finish times in minutes (y) for a 5K footrace.. Interpret the relationship between the variables x and y. a) There is a strong positive correlation. b) There is a weak positi

> A runner tracks her average weekly mileage while marathon training along with her marathon finish times, given by the table below. Classify the correlation between two variables. Weekly Mileage ______ Marathon Time (mins) 55 …â&

> The proportion of the variability in the dependent variable (y) accounted for or explained by the independent variable (x) is called the __________. a) Correlation coefficient b) Regression slope coefficient c) Regression sum of squares d) Coefficient o

> For a least-squares regression line, the sum of the residuals is __________. a) Always zero b) Always positive c) Always negative d) Sometimes positive and sometimes negative 12. Residuals with large magnitudes can be used to located data points that l

> A graphical tool to illustrate the relationship between matched observations of two variables (e.g., y = the annual cost of operating a commercial airliner and x = the annual number of passengers served by the airline), is __________. a) A histogram b) A

> After establishing an overall significant difference between the means of several groups using ANOVA if we want to determine which pairs of means are significant when the sample sizes are unequal, it is appropriate to use __________. a) A series of t-tes

> A process analyst wants to conduct a study to compare five different welding techniques that have been newly developed. Fifty welders, who work in three different shifts, are randomly selected and randomly assigned to try out a welding technique (each op

> To understand how the weights of the cereal boxes vary among four different adjustable stabilizer settings of the rotary valve on the filling machine in three different production shifts, a manufacturing firm collects sample data using a structure or pla

> A manager wants to test if there is a significant difference in the variance of the output from two similar machines. It has been determined that the output of the two machines is normally distributed. To carry out the hypothesis test about the populatio

> A human resources manager wants to conduct a “before/after” study on 16 employees to determine if a motivation seminar results in an increase in their ratings of the company. The after-ratings are subtracted from the b

> To determine whether two brands of car tires differ in their performance measured in terms of the average wear over the first 10,000 miles, we should conduct __________. a) One hypothesis test for the difference in the two population means b) Two hypothe

> A nutritionist for a university wants to determine an average BMI of its students by taking a random sample of 50 students. The standard deviation of the BMIs of population of students is unknown. She is willing to accept a Type I error rate of 0.05. The

> The dean of a business school claims that the average starting salary of its graduates is more than 85 (in $000’s). It is known that the population standard deviation is 10 (in $000’s). Sample data on the starting salaries of 64 randomly selected recent

> A test of the hypotheses, H0: p = 0.18 and H1: p > 0.18 is a __________. a) One-tailed test b) Two-tailed test c) Test of two sample means d) Test of two sample proportions 14. A test of the hypotheses, H0: p = 0.18 and H1: p ≠ 0.18 is a __________. a) O

> All statistical hypotheses consist of two parts, __________ and __________. a) A null hypothesis; a full hypothesis b) A null hypothesis; a substitute hypothesis c) A null hypothesis; an alternate hypothesis d) A null hypothesis; a substantive hypothesis

> A t-distribution is similar to the z-distribution except that __________. a) It is not unimodal b) It is not symmetrical c) It has more area in the tails d) It is not bell-shaped 21. The following random sample was selected from a normal distribution: 4

> 9. In a normal distribution, what values of z should we choose if we want 90% of the area under the curve symmetrically distributed around the mean? a) ( 1.00 b) ( 1.50 c) ( 1.645 d) ( 1.96 10. In a normal distribution, if we consider the range of values

> The luggage weights for passengers for an airline are normally distributed with a mean of 25 lbs., and a standard deviation of 3 lbs. Suppose the limit on the total luggage weight is 2600 lbs. If 100 passengers are taking the airline, what is the probabi

> Suppose samples of size 100 are drawn randomly from a population that has a mean of 20 and a standard deviation of 5. What is the probability of observing a sample mean between 19 and 20.5? a) 0.3413 b) 0.6826 c) 8165 d) 0.1587 e) 0.6587 15. Suppose sa

> Selection of the winning numbers is a lottery is an example of __________. a) Convenience sampling b) Random sampling c) Nonrandom sampling d) Regulatory sampling 7. A random number generator is usually a computer program which allows computer-calculated

> A score on a 15-point multiple choices quiz measuring knowledge of statistics is an example of a(n) a) Nominal b) Ordinal c) Interval d) Ratio e) Exponential 24. Which level of data measurement allows the most or broadest application of statistical techn

> The shape of a symmetrical binomial distribution with large sample size, i.e., a large number of possible outcomes, would most likely look like a __________. a) Rectangle b) Whale c) Bell d) Hockey stick 23. In which of the following cases would the

> All normal distributions can be converted into a single distribution called the __________. a) Universal or U-distribution b) General or G-distribution c) Standard normal or the z- distribution d) Common or C-distribution 14. To convert any x value of a

> If a continuous random variable has a uniform distribution between 20 and 70, the graph of its distribution will be a rectangle with height equal to __________. a) 50 b) 1/50 c) 20 d) 70 3. The values of a random variable are uniformly distributed

> Which of the following is a characteristic of a hypergeometric distribution? a) It is a continuous distribution. b) It has undefined trials c) The outcome of each trial is a success or a failure or undefined. d) Sampling is done without replacement. e)

> In the distribution of a random variable x which is binomial with number of trials n = 30 and the probability of success p = 0.99, the largest value of x that can occur is __________. a) 24 b) 30 c) 15 d) Infinity 14. One fair coin is tossed 10 times, w

> The random variable defined as the “number of people who arrive at a store during a 15-minute interval,” is an example of __________. a) An experimental random variable b) A continuous random variable c) A discrete random variable d) Not a random variabl

> Fifty percent of all technical assistants would like to have a PC. Eighty percent of all technical assistants would like to have MAC. Fourty-five percent of all technical assistants would like to have both. If a technical assistant is randomly selected,

> A fair coin is tossed 4 times and the events A and B are defined as follows: A: {At least More than 2 heads is observed} B: {The number of heads is odd} Use the knowledge of marginal, union, intersection and conditional probabilities to describe the prob

> The method of assigning probabilities based on the laws and rules pertaining to an experiment is called the __________. a) Experimental method b) Classical method c) Relative frequency of occurrence method d) Subjective method 6. If the occurrence of on

> If the sample variance of a dataset of size 8 is 2.57, what is the population variance if considering the same dataset to be a population? a) 2.57 b) 2.28 c) 1.60 d) 1.5 24. If the sample standard deviation of a dataset consisting of 9 observations is 8,

> When you use the data gathered from a sample to generate statistics to reach conclusions about the population from which the sample was taken, you are performing __________. a) Descriptive statistics b) A census c) Inferential statistics d) Constructiv

> A toy-manufacturing company has been given a large order for small plastic whistles that will be given away by a large fast-food hamburger chain with its kid’s meal. Seven random samples of four whistles have been taken. The weight of e

> A food-processing company makes potato chips, pretzels, and cheese chips. Although its products are packaged and sold by weight, the company has been taking sample bags of cheese chips and counting the number of chips in each bag. Shown here is the numbe

> A manufacturer produces digital watches. Every two hours a sample of six watches is selected randomly to be tested. Each watch is run for exactly 15 minutes and is timed by an accurate, precise timing device. Because of the variation among watches, they

> A manufacturing company produces cylindrical tubes for engines that are specified to be 1.20 centimeters thick. As part of the company’s statistical quality control effort, random samples of four tubes are taken each hour. The tubes are

> A fruit juice company sells a glass container filled with 24 ounces of cranapple juice. Inspectors are concerned about the consistency of volume of fill in these containers. Every two hours for three days of production, a sample of five containers is ran

> Examine the Minitab output shown here for a multiple regression analysis. How many predictors were there in this model? Comment on the overall significance of the regression model. Discuss the t ratios of the variables and their significance. Analysis o

> Jensen, Solberg, and Zorn investigated the relationship of insider ownership, debt, and dividend policies in companies. One of their findings was that firms with high insider ownership choose lower levels of both debt and dividends. Shown here is a sampl

> Is there a particular product that is an indicator of per capita personal consumption for countries around the world? Shown here are data on per capita personal consumption, paper consumption, fish consumption, and gasoline consumption for 11 countries.

> Use the following data to determine the equation of the multiple regression model. Comment on the regression coefficients. Predictor _________ Coefficient Constant …………………… 31,409.5 x1 …………………….………… .08425 x2 …………………….………… 289.62 x3 …………………….………… −.0947

> Minitab residual diagnostic output from the multiple regression analysis for the data given in Problem 13.30 follows. Refer to the Problem Data 13.30: Discuss any potential problems with meeting the regression assumptions for this regression analysis

> Shown here are the data for y and three predictors, x1, x2, and x3. A multiple regression analysis has been done on these data; the Minitab results are given. Comment on the outcome of the analysis in light of the data. Regression Analysis: Y versus X1,

> The American Chamber of Commerce Researchers Association compiles cost-of-living indexes for selected metropolitan areas. Shown here are cost-of-living indexes for 25 different cities on five different items for a recent year. Use the data to develop a r

> Using the following data, determine the equation of the regression model. How many independent variables are there? Comment on the meaning of these regression coefficients. Predictor _________ Coefficient Constant ………………….. 121.62 x1 ……………………………... −.174

> The U.S. Department of Agriculture publishes data annually on various selected farm products. Shown here are the unit production figures (in millions of bushels) for three farm products for 10 years during a 20-year period. Use these data and multiple re

> The U.S. Bureau of Labor Statistics produces consumer price indexes for several different categories. Shown here are the percentage changes in consumer price indexes over a period of 20 years for food, shelter, apparel, and fuel oil. Also displayed are t

> Investment analysts generally believe the interest rate on bonds is inversely related to the prime interest rate for loans; that is, bonds perform well when lending rates are down and perform poorly when interest rates are up. Can the bond rate be predic

> The Shipbuilders Council of America in Washington, D.C., publishes data about private shipyards. Among the variables reported by this organization are the employment figures (per 1000), the number of naval vessels under construction, and the number of re

> The U.S. Bureau of Mines produces data on the price of minerals. Shown here are the average prices per year for several minerals over a decade. Use these data and multiple regression to produce a model to predict the average price of gold from the other

> Given here are the data for a dependent variable, y, and independent variables. Use these data to develop a regression model to predict y. Discuss the output.

> Use the following data to develop a multiple regression model to predict y from x1 and x2. Discuss the output, including comments about the overall strength of the model, the significance of the regression coefficients, and other indicators of model fit.

> Study the Excel regression output that follows. How many predictors are there? What is the equation of the regression model? Using the key statistics discussed in this chapter, discuss the strength of the model and its predictors.

> Study the Minitab regression output that follows. How many predictors are there? What is the equation of the regression model? Using the key statistics discussed in this chapter, discuss the strength of the model and the predictors. Regression Analysis:

> Study the Minitab residual diagnostic output that follows. Discuss any potential problems with meeting the regression assumptions for this regression analysis based on the residual graphics.

> Study the Excel output shown in Problem 13.13. Comment on the overall strength of the regression model in light of S, R2, and adjusted R2. Refer in Problem Data 13.13:

> Use a computer to develop the equation of the regression model for the following data. Comment on the regression coefficients. Determine the predicted value of y for x1 = 33, x2 = 29, and x3 = 13.

> Using the regression output obtained by working Problem 13.12, comment on the overall strength of the regression model using S, R2, and adjusted R2.

> A corporation owns several companies. The strategic planner for the corporation believes dollars spent on advertising can to some extent be a predictor of total sales dollars. As an aid in long-term planning, she gathers the following sales and advertisi

> Using the regression output obtained by working Problem 13.11, comment on the overall strength of the regression model using S, R2, and adjusted R2.

> Using the regression output obtained by working Problem 13.6, comment on the overall strength of the regression model using S, R2, and adjusted R2.