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business communication

Questions and Answers of Business Communication

Fill in the blanks. a. A relative-frequency distribution is to a variable as a distribution is to a random variable. b. A relative-frequency histogram is to a variable as a histogram is to a random
Provide an example (other than one discussed in the text) of a random variable that does not arise from a quantitative variable of a finite population in the context of randomness.
How do you graphically portray the probability distribution of a discrete random variable?
Give two reasons why the use of smooth curves to describe shapes of distributions is helpful.
In each of Exercises 1-3, determine whether r is positive, negative, or zero.1.2. 3.
Suppose that a variable of a population has a bell-shaped distribution. If you take a large simple random sample from the population, roughly what shape would you expect the distribution of the
From ESPN MLB Scoreboard, we obtained the following major league baseball scores for August 14, 2013. Is this study descriptive or inferential? Explain your answer. Games in AL stadiums
Fill in the blank. For a discrete random variable, the sum of the probabilities of its possible values equals ______________.
Suppose that you make a large number of independent observations of a random variable and then construct a table giving the possible values of the random variable and the proportion of times each
What rule of probability permits you to obtain any probability for a discrete random variable by simply knowing its probability distribution?
We have drawn a smooth curve that represents a distribution. In each case, do the following:a. Identify the shape of the distribution with regard to modality.b. Identify the shape of the distribution
Two random variables, X and Y, have standard deviations 2.4 and 3.6, respectively. Which one is more likely to take a value close to its mean? Explain your answer.
Determine 0!, 3!, 4!, and 7!.
Fill in the blanks. a. A is a quantitative variable whose value depends on chance. b. A discrete random variable is a random variable whose possible values .
If you sum the probabilities of the possible values of a discrete random variable, the result always equals ____________.
A variable is approximately normally distributed. If you draw a histogram of the distribution of the variable, roughly what shape will it have?
What does the symbol zα signify?
Which normal distribution has a wider spread: the one with mean 1 and standard deviation 2 or the one with mean 2 and standard deviation 1? Explain your answer.
In an issue of Discover (Vol. 26, No. 2, pp. 10-11), J. Netting described the research of E. Tibbetts of the University of Arizona in the article, "The Kind of Face Only a Wasp Could Trust." Tibbetts
The Information Please Almanac provides the number of children of each of the U.S. presidents. A frequency histogram for number of children by president, through President Barack H. Obama, is as
The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 mph and, according to the online document "Cheetah
R. Reifen et al. studied various nutritional measures of Ethiopian school children and published their findings in the paper "Ethiopian-Born and Native Israeli School Children Have Different Growth
The subterranean coruro (Spalacopus cyanus) is a social rodent that lives in large colonies in underground burrows that can reach lengths of up to 600 meters. Zoologists S. Begall and M. Gallardo
From Player Roster, the official roster of the 2013 Super Bowl champion Baltimore Ravens, we obtained the heights, in inches, of the players on that team. A dotplot of those heights is as follows.
Polychlorinated biphenyls (PCBs), industrial pollutants, are known to be carcinogens and a great danger to natural ecosystems. As a result of several studies, PCB production was banned in the United
The Internal Revenue Service (IRS) publishes data on adjusted gross incomes in the document Statistics of Income, Individual Income Tax Returns. The following relative-frequency histogram shows one
If you observe the values of a normally distributed variable for a sample, a normal probability plot should be roughly ___________.
A study published by E. Anionwu et al. in the British Medical Journal (Vol. 282, pp. 283-286) measured the steady-state hemoglobin levels of patients with three different types of sickle cell
The Bureau of Economic Analysis gathers information on the length of stay in Europe and the Mediterranean by U.S. travelers. Data are published in Survey of Current Business. The following
A researcher wants to estimate the average income of parents of college students. To accomplish that, he surveys a sample of 250 students at Yale. Is this a representative sample? Explain your answer.
Explain why the minimum and maximum observations are added to the three quartiles to describe better the variation in a data set.
Is an extreme observation necessarily an outlier? Explain your answer.
Identify by name three important groups of percentiles.
Regarding the interquartile range, a. What type of descriptive measure is it? b. What does it measure?
Identify an advantage that the median and interquartile range have over the mean and standard deviation, respectively.
When are the adjacent values just the minimum and maximum observations?
What are the parameters for a normal curve?
Fill in the blanks: Roughly, when arranged in increasing order, the middle 50% of a data set are found between __________ and __________.
Fill in the blank: Roughly, when arranged in increasing order, the uppermost 25% of a data set are greater than or equal to ________.
Suppose P(A) = 0.6 and P(B | A) = 0.4. Find P(A& B).
In a national poll taken on August 7-11, 2013, by Gallup, Inc., 1039 adults who were employed full or part time were asked the following question: "If you won 10 million dollars in the lottery, would
Suppose P(C) = 0.3 and P(D |C) = 0.8. Find P(C & D).
The area under a particular normal curve to the left of 105 is 0.6227. A normally distributed variable has the same mean and standard deviation as the parameters for this normal curve. What
Give one reason why constructing and reading graphs and charts carefully is important.
Acute rotavirus diarrhea is the leading cause of death among children under age 5, killing an estimated 4.5 million annually in developing countries. Scientists from Finland and Belgium claim that a
If, in Example 6.20, the true-false exam had 30 questions instead of 10, which normal curve would you use to approximate probabilities for the number of correct guesses?
P(B) = 0.8 and P(B | A) = 0.6 Decide whether or not the two events in question are independent or whether it is not possible to tell. Justify your answers.
With which normal distribution is the standard normal curve associated?
Why is the standard normal curve sometimes referred to as the z-curve?
The area under the standard normal curve that lies to the left of a z-score is always strictly between _______________ and _______________.
Explain why assessing the normality of a variable is often important.
In the 1940s and early 1950s, the public was greatly concerned about polio. In an attempt to prevent this disease, Jonas Salk of the University of Pittsburgh developed a polio vaccine. In a test of
Why should you sometimes use normal-curve areas to approximate binomial probabilities even though you have a formula for computing them exactly?
State the two basic properties of every density curve.
For a variable with a density curve, what is the relationship between the percentage of all possible observations of the variable that lie within any specified range and the corresponding area under
Explain the relationship between percentages for a normally distributed variable and areas under the corresponding normal curve.
Identify the distribution of the standardized version of a normally distributed variable.
A curve has area 0.425 to the left of 4 and area 0.585 to the right of 4. Could this curve be a density curve for some variable? Explain your answer.
A curve has area 0.613 to the left of 65 and area 0.287 to the right of 65. Could this curve be a density curve for some variable? Explain your answer.
What key fact permits you to determine percentages for a normally distributed variable by first converting to z-scores and then determining the corresponding area under the standard normal curve?
Does the sample size have an effect on the mean of all possible sample means? Explain your answer.
What is another name for the standard deviation of the variable x̅? What is the reason for that name?
According to a study published in the Journal of the American Public Health Association, lefthanded people do not die at an earlier age than right-handed people, contrary to the conclusion of a
You have seen that the larger the sample size, the smaller the sampling error tends to be in estimating a population mean by a sample mean. This fact is reflected mathematically by the formula for
A variable of a population has mean μ and standard deviation σ. For a large sample size n, fill in the blanks. Justify your answers. a. Approximately ______________% of all possible samples have
Why is sampling often preferable to conducting a census for the purpose of obtaining information about a population?
Find the mean and standard deviation of the variable x̅, given the mean and standard deviation of the population and the sample size.
Although, in general, you cannot know the sampling distribution of the sample mean exactly, by what distribution can you often approximate it?
Find the confidence level and α for a. A 90% confidence interval. b. A 99% confidence interval.
Find the confidence level and α for a. An 85% confidence interval. b. A 95% confidence interval.
For what is normal population an abbreviation?
What is meant by saying that a statistical procedure is robust?
Suppose that you will be taking a random sample from a population and that you intend to find a 95% confidence interval for the population mean, μ. Which sample size, 25 or 50, will result in the
In the article, "One's Sex, Sleep, and Posttraumatic Stress Disorder" (Biology of Sex Differences, Vol. 3, No. 29, pp. 1-7), I. Kobayashi et al. study the relationship between one's sex, sleep
Discuss the relationship between the margin of error and the standard error of the mean.
In estimating the mean monthly fuel expenditure, μ, per household vehicle, the Energy Information Administration takes a sample of size 6841. Assuming that σ = $20.65, determine the margin of error
Why do you need to consider the studentized version of x̅ to develop a confidence-interval procedure for a population mean when the population standard deviation is unknown?
Although, in practice, sample data are generally analyzed in inferential studies, what is the ultimate objective of such studies?
For a given brand of microwave popcorn, what property is desirable for the population standard deviation of the cooking time? Explain your answer.
A variable of a population has a normal distribution. Suppose that you want to find a confidence interval for the population mean. a. If you know the population standard deviation, which procedure
Identify the statistic that is used to estimate a. A population mean. b. A population standard deviation.
Earlier in this section, we found that the population mean length of the holes at the Augusta National Golf Club is 413.1 yd. In this context, is the number 413.1 a parameter or a statistic? Explain
Earlier in this section, we found that the population standard deviation of the lengths of the holes at the Augusta National Golf Club is 132.0 yd. In this context, is the number 132.0 a parameter or
The value of a statistic used to estimate a parameter is called a _________ of the parameter.
Why is probability theory important to statistics?
In the article by P. Ridker et al. titled "A Randomized Trial of Low-dose Aspirin in the Primary Prevention of Cardiovascular Disease inWomen" (New England Journal of Medicine, Vol. 352, pp.
When estimating an unknown parameter, what does the margin of error indicate?
In Example 4.21 on page 194, we discussed randomly selecting, without replacement, two students from Professor Weiss's introductory statistics class. Suppose now that three students are selected
Express the form of most of the confidence intervals that you will encounter in your study of statistics in terms of "point estimate" and "margin of error."
Suppose that you take 1000 simple random samples from a population and that, for each sample, you obtain a 95% confidence interval for an unknown parameter. Approximately how many of those confidence
Suppose that you take 500 simple random samples from a population and that, for each sample, you obtain a 90% confidence interval for an unknown parameter. Approximately how many of those confidence
A simple random sample is taken from a population and yields the following data for a variable of the population:Find a point estimate for the population mean (i.e., the mean of the variable).
What does it mean for four events to be exhaustive?
What does it mean for four events to be mutually exclusive?
If you obtained one thousand 95% confidence intervals for a population mean, μ, roughly how many of the intervals would actually contain μ?
Research by G. Visser and C. Barker in "A Geography of British Backpacker Tourists in South Africa" (Geography, Vol. 89, No. 3, pp. 226-239) reflected on the impact of British backpacker tourists
What distributional assumption must be met in order to use the Wilcoxon signed-rank test?
We mentioned that if, in a Wilcoxon signed-rank test, an observation equals μ0 (the value given for the mean in the null hypothesis), that observation should be removed and the sample size reduced
Explain how to proceed with a sign test if one or more of the observations equals η0, the value specified in the null hypothesis for the population median.
Why don't hypothesis tests always yield correct decisions?

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