Chapter 01 - An Introduction to Business Statistics

CHAPTER 1—An Introduction to Business Statistics

1.1 A population is a set of existing units.
Consumers utilizing a particular product.

1.2 Any characteristic of a population unit is called a variable.
Quantitative: values on the real number line.
Qualitative: record unit into categories.

1.3 a. Quantitative; dollar amounts correspond to values on the real number line.

b. Quantitative; net profit is a dollar amount.

c. Qualitative; which stock exchange is a category.

d. Quantitative; national debt is a dollar amount.

e. Qualitative; media is categorized into radio, television, or print.

1.4 Census: examine all of the population units.
Sample: subset of the units in a population.

1.5 a. Descriptive statistics: science of describing the important aspects of a set of measurements.

b. Statistical inference: science of using a sample of measurements to make generalizations about the important aspects of a population of measurements.

c. Random sample: selected in a manner so that on each selection from the population every unit remaining in the population on that selection has the same chance of being chosen.

d. Systematic sample: select every nth unit of a population.

1.6 Choosing the sample without replacement guarantees that all of the units in the sample will be different units.

1.7 From Table 1.1 (starting in the upper lefthand corner) we obtain the following 2digit random numbers:

33 03 92 85 08 51 60 94 58 09 14 74 24 87 07

Crossing out numbers greater than 27 (because there are only 27 companies), the sample consists of firms 03, 08, 09, 14, and 07. That is:

03 Coca-Cola 09 Reynolds American

07 Sara Lee 14 Pepsi Bottling Group

08 Coca-Cola Enterprises

1.8 From Table 1.1 (starting in the upper righthand corner) we obtain the following 2digit random numbers:

88 22 52 68 07 19 57 51 49 04 12 92 51 10

Crossing out numbers greater than 30 (because there are only 30 companies listed), the sample consists of industries 22, 07, 19, 04, and 10. That is:

22 Toyota Motor 07 General Electric 19 Qualcomm

04 Continental Airlines 10 Illinois Tool Works

1.9 a. From Table 1.1 (starting in the upper left-hand corner) we obtain 5-digit random numbers:
33276 03427 92737 85689 08178
51259 60268 94904 58586 09998
14346 74103 24200 87308 07351
Crossing out the numbers greater than 73,219 (because there are only 73,219 registration cards), the first ten registration cards in the sample are cards:
33276 03427 08178 51259 60268
58586 09998 14346 24200 07351

b. Most of the scores would fall between 36 and 48 because 36 is the smallest score in the sample and 48 is the largest score in the sample. An estimate of the proportion of scores that would be at least 42 is 46/65 = 0.708 because 46 of the 65 sample scores are at least 42.

1.10 Most waiting times will be from .4 to 11.6 minutes. An estimate of the proportion of waiting times less than 6 minutes is found by counting the number of customers with waiting times less than 6 minutes and dividing by the total of 100 customers.

1.11 a. People who oppose TV sex and violence would be most likely to respond.
Yes, almost all respondents are concerned about sex, language, and violence.

b. It is doubtful that a random sample would give the same results. Given the number of people who watch shows containing sex, vulgar language, and violence, it is doubtful that 96 to 97 percent of the population is concerned about sex, language, and violence on TV.

c. It is highly doubtful that 90% of the general population desires a V-chip.

1.12 a. Plot is in statistical control: center can be represented by a horizontal line and spread around the line remains constant over time.

b. Basing the limits on the minimum and maximum temperatures observed, the lower limit is 152 degrees and the upper limit is 170 degrees.


1.13 a. Yes, in control. There is constant variation at a horizontal level.

b. Most breaking strengths will be between 46.8 lbs and 54 lbs.

1.14 Yes, the waiting times are in control. There is reasonably constant variation at a horizontal level.

1.15 A ratio variable is a quantitative variable measured on a scale such that ratios of values of the variables are meaningful and there is an inherently defined zero value. An interval variable is a quantitative variable such that ratios of values of the variable are not meaningful and there is not an inherently defined zero value.

1.16 An ordinal variable is a qualitative variable such that there is a meaningful ordering, or ranking, of the categories. A nominative variable is a qualitative variable such that there is no meaningful ordering, or ranking, of the categories.

1.17 Ordinal, nominative, ordinal, nominative, ordinal, and nominative.

1.18 Nominative, ordinal, ordinal, ordinal, nominative, and nominative.

1.19 When the population consists of two or more groups that differ with respect to the variable of interest.
Strata are nonoverlapping groups of similar units.
Strata should be chosen so that the units in each strata are similar on some characteristic (often a categorical variable).

1.20 Cluster sampling is often used when selecting a sample from a large geographical region.
Because at each stage we “cluster” units into subpopulations.

1.21 First divide 1853 by 100 and round down to 18. We randomly select 1 company from the first 18 (in a list of all the companies). From the company selected we simply count down 18 to get to the next company to select. We continue this process until we have reached a sample size of 100.

1.22 A stratified random sample is selected by dividing the population into some number of strata, and then randomly sampling inside each strata.
Potential strata: students who live off campus and
students who live on campus.

1.23 List all cities with population > 10,000.
In each city, randomly select a number of city blocks.
In each city block, take a random sample of individuals.

1.24 The response variable is whether or not the person has cancer. The factors or independent variables are age, sex, occupation, and number of cigarettes smoked per day. This is an observational study.


1.25 Undercoverage—when some groups in the population are left out of the process of choosing the sample.
Nonresponse—no data obtained from a unit selected in a sample.
Response bias—when a sampling procedure systematically favors certain outcomes.

1.26 Sample may be biased because it is not stated that the recipients of the survey were chosen at random. In addition there may be errors of undercoverage and nonresponse.

1.27 Voluntary response surveys usually give bias results.
Percentage of population that opposes the law probably < 78%.

1.28 His comments are justified because voluntary response surveys are usually biased.

1.29 Using Table 1.1 and starting in column #3 we get the following random numbers:
79 69 33 52 13 16 19 04 14 06 30 25 38 00
Numbering the companies from 00 to 34 this process yields a random sample of size 10.

1.30 The process is not in statistical control and the higher percentages of people waiting too long occur early in the week. A potential solution is to staff at a higher level early in the week.

1.31 Basic cable rates are increasing in a linear fashion on an annual basis.

1.32 Yes. Pre–1959 level of wins appears higher than post–1959 level of wins.

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