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Sampling and Data

Sampling is the process of gathering a subset of data from a population. The information is obtained through a direct method (such as random or non-random selection) or indirect method (e.g. from a larger sample). Sampling is a necessary step in many statistical procedures. It is also used in science to infer properties of a population which cannot be directly measured, such as those of a disease or economic index. Data is information that represents the measurements of a physical quantity, that has been obtained by sampling.

Definitions of Statistics, Probability, and Key Terms

211 Practice Problems
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02:36
Essentials of Statistics for Business and Economics

Figure 1.8 provides a bar chart showing the amount of federal spending for the years 2002 to $2008(\text {USA Today}, \text { February } 5,2008$ ).
a. What is the variable of interest?
b. Are the data categorical or quantitative?
c. Are the data time series or cross-sectional?
d. Comment on the trend in federal spending over time.

Data and Statistics
Ahmad Reda
01:44
Statistics for Business Economics

Fresh fruit price and quantity data for the years 1988 and 2007 follow (Census Bureau website, March 19,2009 ). Quantity data reflect per capita consumption in pounds and prices are per pound.
$$\begin{array}{lccc}
& \text { 1988 per Capita } & \text { 1988 Price } & \text { 2007 Price } \\
\text { Fruit } & \text { Consumption (pounds) } & \text { (\$/pound) } & \text { (\$/pound) } \\
\text { Bananas } & 24.3 & .41 & .53 \\
\text { Apples } & 19.9 & .71 & 1.12 \\
\text { Oranges } & 13.9 & .56 & .91 \\
\text { Pears } & 3.2 & .64 & 1.27
\end{array}$$
a. Compute a price relative for each product.
b. Compute a weighted aggregate price index for fruit products. Comment on the change in fruit prices over the 19 -year period.

Index Numbers
Adriano Chikande
01:17
Statistics for Business Economics

Boran Stockbrokers, Inc., selects four stocks for the purpose of developing its own index of stock market behavior. Prices per share for a 2007 base period, January 2009 , and March 2009 follow. Base-year quantities are set on the basis of historical volumes for the four stocks.
Use the 2007 base period to compute the Boran index for January 2009 and March 2009 Comment on what the index tells you about what is happening in the stock market.

Index Numbers
Adriano Chikande

Data, Sampling, and Variation in Data and Sampling

167 Practice Problems
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01:15
Statistics for Business Economics

A trucking firm handles four commodities for a particular distributor. Total shipments for the commodities in 1994 and $2009,$ as well as the 1994 prices, are reported in the following table.
Develop a weighted aggregate quantity index with a 1994 base. Comment on the growth or decline in quantities over the $1994-2009$ period.

Index Numbers
Adriano Chikande
05:24
Statistics for Business Economics

Draw a graph for the standard normal distribution. Label the horizontal axis at values of $-3,-2,-1,0,1,2,$ and $3 .$ Then use the table of probabilities for the standard normal distribution inside the front cover of the text to compute the following probabilities.
a. $ P(z \leq 1.5)$
b. $ P(z \leq 1)$
c. $ P(1 \leq z \leq 1.5)$
d. $P(0<z<2.5)$

Continuous Probability Distributions
Michael Nartey
05:08
Statistics for Business Economics

Consider a finite population with five elements labeled $A, B, C, D,$ and $E .$ Ten possible simple random samples of size 2 can be selected.
a. List the 10 samples beginning with $\mathrm{AB}, \mathrm{AC},$ and so on.
b. Using simple random sampling, what is the probability that each sample of size 2 is selected?
c. Assume random number 1 corresponds to $A$, random number 2 corresponds to $B$, and so on. List the simple random sample of size 2 that will be selected by using the random digits 8057532.

Sampling and Sampling Distributions
Ryan Mcalister

Frequency, Frequency Tables, and Levels of Measurement

101 Practice Problems
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01:38
Statistics for Business Economics

Average hourly wages for production workers in February 1996 were $\$ 11.86 ;$ in February $2009,$ they were $\$ 18.55 .$ The CPI in February 1996 was $154.9 ;$ in February 2009 it was 212.2
a. Deflate the hourly wage rates in 1996 and 2009 to find the real wage rates.
b. What is the percentage change in actual hourly wages from 1996 to $2009 ?$
c. What is the percentage change in real wages from 1996 to $2009 ?$

Index Numbers
Adriano Chikande
01:30
Statistics for Business Economics

The following table reports prices and usage quantities for two items in 2007 and 2009$$\begin{array}{ccccc}
& {\text { Quantity }} & & \ \ \ {\text { Unit Price (\$) }} \\
\text { Item } & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} & \mathbf{2 0 0 7} & \mathbf{2 0 0 9} \\
\text { A } & 1500 & 1800 & 7.50 & 7.75 \\
\text { B } & 2 & 1 & 630.00 & 1500.00
\end{array}$$
a. Compute price relatives for each item in 2009 using 2007 as the base period.
b. Compute an unweighted aggregate price index for the two items in 2009 using 2007 as the base period.
c. Compute a weighted aggregate price index for the two items using the Laspeyres method.
d. Compute a weighted aggregate price index for the two items using the Paasche method.

Index Numbers
Adriano Chikande
07:23
Statistics for Business Economics

A doctor's office staff studied the waiting times for patients who arrive at the office with a request for emergency service. The following data with waiting times in minutes were collected over a one-month period.
$$2 \quad 5 \quad 10 \quad 12 \quad 4 \quad 4 \quad 5 \quad 17 \quad 11 \quad 8 \quad 9 \quad 8 \quad 12 \quad 21 \quad 6 \quad 8 \quad 7 \quad 13 \quad 18 \quad 3$$
Use classes of $0-4,5-9,$ and so on in the following:
a. Show the frequency distribution.
b. Show the relative frequency distribution.
c. Show the cumulative frequency distribution.
d. Show the cumulative relative frequency distribution.
e. What proportion of patients needing emergency service wait 9 minutes or less?

Descriptive Statistics: Tabular and Graphical Presentations
Pratyush Raitan

Experimental Design and Ethics

38 Practice Problems
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0:00
Mathematical Statistics with Applications

An experiment is to be conducted to compare the effect of digitalis on the contraction of the heart muscles of rats. The experiment is conducted by removing the heart from a live rat, slicing the heart into thin layers, and treating the layers with dosages of digitalis. The muscle contraction is then measured. If four dosages, $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D},$ are to be employed, what advantage might be derived by applying $\mathrm{A}, \mathrm{B}, \mathrm{C},$ and $\mathrm{D}$ to a slice of tissue from the heart of each rat? What principle of design is illustrated by this example?

Considerations in Designing Experiments
Some Elementary. Experimental Designs
0:00
Mathematical Statistics with Applications

Two drugs, A and B, are to be applied to five rats each. Suppose that the rats are numbered from 1
to $10 .$ Use the random number table to assign the rats randomly to the two treatments.

Considerations in Designing Experiments
Some Elementary. Experimental Designs
04:03
Statistics Informed Decisions Using Data

How does the completely randomized design differ from a randomized complete block design?

Comparing Three or More Means
The Randomized Complete Block Design
Mahnoor Khan

Data Collection Experiment

25 Practice Problems
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01:14
Statistics for Business Economics

Under the last-in first-out (LIFO) inventory valuation method, a price index for inventory must be established for tax purposes. The quantity weights are based on year-ending inventory levels. Use the beginning-of-the-year price per unit as the base-period price and develop a weighted aggregate index for the total inventory value at the end of the year. What type of weighted aggregate price index must be developed for the LIFO inventory valuation?
$$\begin{array}{cccc}
& \text { Ending } & {\quad \quad \quad \quad\quad\quad\quad\quad\quad \text { Unit Price (\$) }} \\
\text { Product } & \text { Inventory } & \text { Beginning } & \text { Ending } \\
\text { A } & 500 & .15 & .19 \\
\text { B } & 50 & 1.60 & 1.80 \\
\text { C } & 100 & 4.50 & 4.20 \\
\text { D } & 40 & 12.00 & 13.20
\end{array}$$

Index Numbers
Adriano Chikande
02:47
Statistics for Business Economics

During the 2003 season, Major League Baseball took steps to speed up the play of baseball games in order to maintain fan interest (CNN Headline News, September 30,2003 ). The following results come from a sample of 60 games played during the summer of 2002 and a sample of 50 games played during the summer of $2003 .$ The sample mean shows the mean duration of the games included in each sample.
$$\begin{array}{cc}2002 \text { Season } & 2003 \text { Season } \\ n_{1}=60 & n_{2}=50 \\ \bar{x}_{1}=2 \text { hours, } 52 \text { minutes } & \bar{x}_{2}=2 \text { hours }, 46 \text { minutes }\end{array}$$
a. A research hypothesis was that the steps taken during the 2003 season would reduce the population mean duration of baseball games. Formulate the null and alternative hypotheses.
b. What is the point estimate of the reduction in the mean duration of games during the 2003 season?
c. Historical data indicate a population standard deviation of 12 minutes is a reasonable assumption for both years. Conduct the hypothesis test and report the $p$ -value. At a .05 level of significance, what is your conclusion?
d. Provide a $95 \%$ confidence interval estimate of the reduction in the mean duration of
games during the 2003 season.
e. What was the percentage reduction in the mean time of baseball games during the 2003 season? Should management be pleased with the results of the statistical analysis? Discuss. Should the length of baseball games continue to be an issue in future years? Explain.

Inference About Means and Proportions with Two Populations
Adriano Chikande
03:00
Statistics for Business and Economics

The Gallup organization conducted a telephone survey with a randomly selected national sample of 1005 adults, 18 years and older. The survey asked the respondents, "How would you describe your own physical health at this time?" (www.gallup.com, February 7,2002 ). Response categories were Excellent, Good, Only Fair, Poor, and No Opinion.
a. What was the sample size for this survey?
b. Are the data qualitative or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, $29 \%$ said their personal health was excellent. How many individuals provided this response?

Data and Statistics
Sandra Kudolo

Sampling Experiment

79 Practice Problems
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01:53
Statistics for Business Economics

Medical tests were conducted to learn about drug-resistant tuberculosis. Of 142 cases tested in New Jersey, 9 were found to be drug-resistant. Of 268 cases tested in Texas, 5 were found to be drug-resistant. Do these data suggest a statistically significant difference between the proportions of drug-resistant cases in the two states? Use a .02 level of significance. What is the $p$ -value, and what is your conclusion?

Inference About Means and Proportions with Two Populations
Adriano Chikande
01:39
Statistics for Business Economics

Consider the following results for independent samples taken from two populations.
$$\begin{array}{ll}
\text { Sample } 1 & \text { Sample } 2 \\
n_{1}=400 & n_{2}=300 \\
\bar{p}_{1}=.48 & \bar{p}_{2}=.36
\end{array}$$
a. What is the point estimate of the difference between the two population proportions?
b. Develop a $90 \%$ confidence interval for the difference between the two population proportions.
c. Develop a $95 \%$ confidence interval for the difference between the two population proportions.

Inference About Means and Proportions with Two Populations
Adriano Chikande
01:24
Statistics for Business Economics

Condé Nast Traveler conducts an annual survey in which readers rate their favorite cruise ship. All ships are rated on a 100 -point scale, with higher values indicating better service. A sample of 37 ships that carry fewer than 500 passengers resulted in an average rating of $85.36,$ and a sample of 44 ships that carry 500 or more passengers provided an average rating of 81.40 (Condé Nast Traveler, February 2008 ). Assume that the population standard deviation is 4.55 for ships that carry fewer than 500 passengers and 3.97 for ships that carry
500 or more passengers.
a. What is the point estimate of the difference between the population mean rating for ships that carry fewer than 500 passengers and the population mean rating for ships that carry 500 or more passengers?
b. $\quad$ At $95 \%$ confidence, what is the margin of error?
c. What is a $95 \%$ confidence interval estimate of the difference between the population mean ratings for the two sizes of ships?

Inference About Means and Proportions with Two Populations
Adriano Chikande

Sample Surveys

15 Practice Problems
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05:12
Understandable Statistics, Concepts and Methods

General: Completely Randomized Experiment How would you use a completely randomized experiment in each of the following settings? Is a placebo being used or not? Be specific and give details.
(a) A veterinarian wants to test a strain of antibiotic on calves to determine their resistance to common infection. In a pasture are 22 newborn calves. There is enough vaccine for 10 calves. However, blood tests to determine resistance to infection can be done on all calves.
(b) The Denver Police Department wants to improve its image with teenagers. A uniformed officer is sent to a school 1 day a week for 10 weeks. Each day the officer visits with students, eats lunch with students, attends pep rallies, and so on. There are 18 schools, but the police department can visit only half of these schools this semester. A survey regarding how teenagers view police is sent to all 18 schools at the end of the semester.
(c) A skin patch contains a new drug to help people quit smoking. A group of 75 cigarette smokers have volunteered as subjects to test the new skin patch. For 1 month, 40 of the volunteers receive skin patches with the new drug. The other volunteers receive skin patches with no drugs. At the end of 2 months, each subject is surveyed regarding his or her current smoking habits.

Getting Started
Introduction to Experimental Design
Sneha Ravi
01:54
Understandable Statistics, Concepts and Methods

General: Gathering Data Which technique for gathering data (sampling, experiment, simulation, or census) do you think was used in the following studies?
(a) An analysis of a sample of 31,000 patients from New York hospitals suggests that the poor and the elderly sue for malpractice at one-fifth the rate of wealthier patients (Journal of the American Medical Association).
(b) The effects of wind shear on airplanes during both landing and takeoff were studied by using complex computer programs that mimic actual flight.
(c) A study of all league football scores attained through touchdowns and field goals was conducted by the National Football League to determine whether field goals account for more scoring events than touchdowns (USA Today).
(d) An Australian study included 588 men and women who already had some precancerous skin lesions. Half got a skin cream containing a sunscreen with a sun protection factor of $17 ;$ half got an inactive cream. After 7 months, those using the sunscreen with the sun protection had fewer new precancerous skin lesions (New England Journal of Medicine).

Getting Started
Introduction to Experimental Design
Sneha Ravi
02:05
Understandable Statistics, Concepts and Methods

In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give examples of population members that might have been omitted.
(a) The population consists of all 250 students in your large statistics class. You plan to obtain a simple random sample of 30 students by using the sampling frame of students present next Monday.
(b) The population consists of all 15 -year-olds living in the attendance district of a local high school. You plan to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame.

Getting Started
Random Samples
Harsh Gadhiya

Standard Error

2 Practice Problems
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04:08
Statistics

Complete the following table for the coin-tossing game.

Chance Errors in Sampling
Bryan Luo
01:37
Statistics

A simple random sample of $3,500$ people age 18 or over is taken in a large
town to estimate the percentage of people (age 18 and over in that town) who
read newspers. It turns out that $2,487$ people in the sample are newspaper
readers. 12 The population percentage is estimated as
$$
\frac{2,487}{3,500} \times 100 \% \approx 71 \%
$$
The standard error is estimated as 0.8 of $1 \%,$ because
$$
\sqrt{3,500} \times \sqrt{0.71 \times 0.29} \approx 27, \quad \frac{27}{3,500} \times 100 \% \approx 0.8 \text { of } 1 \%
$$
$$
\begin{array}{l}{\text { (a) Is } 0.8 \text { of } 1 \% \text { the right SE? Answer yes or no, and explain. }} \\ {\text { (b) } 71 \% \pm 1.6 \% \text { is a }}\end{array}
$$

The Accuracy of Percentages
Eleanor Archer

Qualitative and Quantitative Variables

7 Practice Problems
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03:55
Statistics Informed Decisions Using Data

Contrast the differences between qualitative and quantitative variables.

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya
00:21
Statistics Informed Decisions Using Data

What type of variable is required when drawing a time-series plot? Why do we draw time-series plots?

Organizing and Summarizing Data
Additional Displays of Quantitative Data
Hossam Mohamed
00:23
Statistics Informed Decisions Using Data

Classify the variable as qualitative or quantitative.
Phone number

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya

Discrete and Continuous Variables

8 Practice Problems
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00:53
Statistics Informed Decisions Using Data

The age of a person is commonly considered to be a continuous random variable. Could it be considered a discrete random variable instead? Explain.

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya
01:46
Statistics Informed Decisions Using Data

Discuss the differences between discrete and continuous variables.

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya
00:21
Statistics Informed Decisions Using Data

Determine whether the quantitative variable is discrete or continuous.
Length (in minutes) of a country song

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya

Level of Measurement of a Variable

7 Practice Problems
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01:43
Statistics Informed Decisions Using Data

In your own words, define the four levels of measurement of a variable. Give an example of each.

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya
00:27
Statistics Informed Decisions Using Data

Determine the level of measurement of each variable.
Eye color

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya
00:22
Statistics Informed Decisions Using Data

Determine the level of measurement of each variable.
Highest degree conferred (high school, bachelor's, and so on)

Data Collection
Introduction to the Practice of Statistics
Harsh Gadhiya

Various Types of Observational Studies

3 Practice Problems
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02:31
Statistics Informed Decisions Using Data

The following abstract appears in The New England Journal of Medicine:
BACKGROUND. The relation between passive smoking and lung cancer is of great public health importance. Some previous studies have suggested that exposure to environmental tobacco smoke in the household can cause lung cancer, but others have found no effect. Smoking by the spouse has been the most commonly used measure of this exposure. METHODS. In order to determine whether lung cancer is associated with exposure to tobacco smoke within the household, we conducted a case-control study of 191 patients with lung cancer who had never smoked and an equal number of persons without lung cancer who had never smoked. Lifetime residential histories including approximately 17 percent of lung cancers among nonsmokers information on exposure to environmental tobacco smoke can be attributed to high levels of exposure to cigarette were compiled and analyzed. Exposure was measured in smoke during childhood and adolescence. terms of "smoker-years;" determined by multiplying the (a) What is the research objective? number of years in each residence by the number of smokers in the houschold. RESULTS. Houschold cxposurc to 25 or morc smokcr-ycars
(c) What is the response variable in the study? Is it during childhood and adolescence doubled the risk of lung cancer. Approximately 15 percent of the control subjects who
(d) What is the explanatory variable in the study? Is it had never smoked reported this level of exposure. Household exposure of less than 25 smoker-years during childhood and adolescence did not increase the risk of lung cancer. Exposure to a spouse's smoking, which constituted less than one third $\quad$ (f) What is the conclusion of the study? Can we conclude of total household exposure on average, was not associated that exposure to smoke in the household causes lung with an increase in risk. CONCLUSIONS. The possibility of recall bias and other
(g) Would it be possible to design an experiment to answer methodological problems may influence the results of case the research question in part (a)? Explain. control studies of environmental tobacco smock. Nonetheless. our findings regarding exposure during Carly life suggest that

Data Collection
Observational Studies versus Designed Experiments
Harsh Gadhiya
01:39
Statistics Informed Decisions Using Data

Write a summary of the following opinion. The opinion was posted at abcnews.com. Include the type of study conducted, possible lurking variables, and conclusions. What is the message of the author of the article?
New Research May Couse More Fear Than Warranted. One Physician Explains OPINION by JOSEPH MOORE, M.D. A recent study out of Switzerland indicates there might be an increased risk of certain blood cancers in people with prolonged exposure to electromagnetic fields, like those generated from high-voltage power lines. If you live in a house near one of these high-voltage power lines. a study like this one might make you wonder whether you should move. But based on what we know now, I don't think that's necessary. We can never say there is no risk, but we can say that the risk appears to be extremely small.
-Scare Science" The results of studies like this add a bit more to our knowledge of potential harmful environmental exposures, but they should also be seen in conjunction with the results of hundreds of studies that have gone before. It cannot be seen as a definitive call to action in and of itself. The current study followed more than 20,000 Swiss railway workers over a period of 30 years. True, that represents a lot of people over a long period of time. However, the problem with many epidemiological studies, like this one, is that it is difficult to have an absolute control group of people to compare results with. The researchers compared the incidence of different cancers of workers with a high amount of electromagnetic field exposure to those workers with lower exposures. These studies aren't like those that have identified definitive links between an exposure and a disease Ike those involving smoking and lung cancer. In those studies. we can actually measure the damage done to lung tissue as a direct result of smoking. But usually it's very difficult for the conclusions of an epidemiological study to rise to the level of controlled studies in determining public policy. Remember the recent scare about coffee and increased risk of pancreatic cancer? Or the always simmering issue of cell phone use and brain tumors?
As far as I can tell, none of us have turned in our cell phones. In our own minds, we've decided that any links to cell phone use and brain cancer have not been proven definitively. While we can't say that there is absolutely no risk in using cell phones. individuals have determined on their own that the potential risks appear to be quite small and are outweighed by the benefits.
Findings Shouldn't Lead to Fear As a society, we should continue to investigate these and other related exposures to try to prove one way or another whether they are disease-causing. If we don't continue to study. we won't find out. It's that simple. When findings like these come out, and l'm sure there will be more in the future. I would advise people not to lose their heads. Remain calm. You should take the results as we scientists do - as intriguing pieces of data about a problem we will eventually learn more about, either positively or negatively, in the future. It should not necessarly alter what we do right now. What we can do is take actions that we know will reduce our chances of developing cancer. Stop smoking and avoid passive smoke. It is the leading cause of cancer that individuals have control over. Whenever you go outside, put on sunscreen or cover up. Eat a heaithy diet and stay physically active. Make sure you get tested or screened. Procedures like colonoscopies. mammograms. pap smears and prostate exams can catch the early signs of cancer. when the chances of successfully treating them are the best. Taking the actions above will go much farther in reducing your risks for cancer than moving away from power lines or throwing away your cell phone.

Dr. Joseph Moore is a medical oncologist at Duke University Comprehensive Cancer Center. Source:
Reprinted with the permission of the author.

Data Collection
Observational Studies versus Designed Experiments
Harsh Gadhiya
02:24
Statistics Informed Decisions Using Data

What is a cross-sectional study? What is a case-control study? Which is the superior observational study? Why?

Data Collection
Observational Studies versus Designed Experiments
Harsh Gadhiya

Simple Random Sampling

15 Practice Problems
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02:22
Statistics Informed Decisions Using Data

Putting It Together: Thinking about Randomness What is random sampling? Why is it necessary for a sample to be obtained randomly rather than conveniently? Will randomness guarantee that a sample will provide accurate information about the population? Explain.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya
00:30
Statistics Informed Decisions Using Data

Worker Morale The owner of a private food store is concerned about employee morale. She decides to survey the employees to see if she can learn about work environment and job satisfaction. Obtain a simple random sample of size 5 from the names in the given table. Write a short description of the process you used to generate your sample.
(TABLE CANNOT COPY)

Data Collection
Simple Random Sampling
Hossam Mohamed
01:15
Statistics Informed Decisions Using Data

Obtaining a Simple Random Sample Suppose the mayor of Justice, Illinois, asks you to poll the residents of the village. The mayor provides you with a list of the names and phone numbers of the 5832 residents of the village.
(a) Discuss the procedure you would follow to obtain a simple random sample of 20 residents.
(b) Obtain this sample.

Data Collection
Simple Random Sampling
Hossam Mohamed

Sampling Methods

21 Practice Problems
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01:17
Statistics Informed Decisions Using Data

Research the origins of the Gallup Poll and the current sampling method the organization uses. Report your findings to the class.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya
02:04
Statistics Informed Decisions Using Data

Putting It Together: Comparing Sampling Methods Suppose a political strategist wants to get a sense of how American adults aged 18 years or older feel about health care and health insurance.
(a) In a political poll, what would be a good frame to use for obtaining a sample?
(b) Explain why simple random sampling may not guarantee that the sample has an accurate representation of registered Democrats, registered Republicans, and registered Independents.
(c) How can stratified sampling guarantee this representation?

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya
01:04
Statistics Informed Decisions Using Data

Sample Design A marketing executive for Coca-Cola, Inc., wants to identify television shows that people in the Boston area who typically drink Coke are watching. The executive has a list of all households in the Boston area. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya

Stratified Sampling

1 Practice Problems
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01:12
Statistics Informed Decisions Using Data

Describe a circumstance in which stratified sampling would be an appropriate sampling method.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya

Systematic Sampling

4 Practice Problems
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01:43
Statistics Informed Decisions Using Data

Systematic Sample To predict the outcome of a county election, a newspaper obtains a list of all 945,035 registered voters in the county and wants to conduct a systematic sample.
(a) Determine $k$ if the sample size is $130 .$
(b) Determine the individuals who will be administered the survey. More than one answer is possible.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya
01:44
Statistics Informed Decisions Using Data

Systematic Sample The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4502 employees at the company and wants to conduct a systematic sample.
(a) Determine $k$ if the sample size is $50 .$
(b) Determine the individuals who will be administered the survey. More than one answer is possible.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya
02:06
Statistics Informed Decisions Using Data

A salesperson obtained a systematic sample of size 20 from a list of 500 clients. To do so, he randomly selected a number from 1 of $25,$ obtaining the number $16 .$ He included in the sample the 16th client on the list and every 25 th client thereafter. List the numbers that correspond to the 20 clients selected.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya

Cluster Sampling

1 Practice Problems
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01:22
Statistics Informed Decisions Using Data

A quality-control expert wishes to obtain a cluster sample by selecting 10 of 795 clusters. She numbers the clusters from 1 to $795 .$ Using Table I from Appendix $A,$ she closes her eyes and drops a pencil on the table. It points to the digit in row 8 column $38 .$ Using this position as the starting point and proceeding downward, determine the numbers for the 10 clusters selected.

Data Collection
Other Effective Sampling Methods
Harsh Gadhiya

Sampling Errors and Non-sampling Errors

3 Practice Problems
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03:03
Statistics Informed Decisions Using Data

Develop a survey that you could administer using online survey tools such as StatCrunch, surveymonkey.com, or polldaddy.com. Administer the survey. Did the responses accurately reflect the goals of each question? What types of nonsampling error did you encounter in the survey? If you invited individuals to take the survey via an e-mail, what type of response rate did you obtain? What approach did you take to increase response rate?

Data Collection
Bias in Sampling
Harsh Gadhiya
03:29
Statistics Informed Decisions Using Data

During every election, pollsters conduct exit polls to help determine which candidate people voted for. During the 2004 presidential election, pollsters incorrectly predicted John Kerry the winner over George Bush. When asked how this error could have happened, the pollsters cited interviewer error due to the fact that many of the interviewers were young, only young voters agreed to be interviewed, and young voters tended to favor Kerry. Plus, young interviewers tend to make more dataentry mistakes. In addition, the method of selecting individuals to be interviewed led to selecting a higher proportion of female voters, and Kerry was favored by females. In some precincts, interviewers were denied access to voters. Research the 2004 exit polling fiasco. Explain which nonsampling errors led to the incorrect conclusion regarding the 2004 election.

Data Collection
Bias in Sampling
Harsh Gadhiya
03:37
Statistics Informed Decisions Using Data

Distinguish between nonsampling error and sampling error.

Data Collection
Bias in Sampling
Harsh Gadhiya

Sampling Bias

11 Practice Problems
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01:42
Statistics Informed Decisions Using Data

Why is a high response rate desired? How would a low response rate affect survey results?

Data Collection
Bias in Sampling
Harsh Gadhiya
01:28
Statistics Informed Decisions Using Data

Name two biases that led to the Literary Digest making an incorrect prediction in the presidential election of 1936.

Data Collection
Bias in Sampling
Harsh Gadhiya
00:37
Statistics Informed Decisions Using Data

The Telephone Consumer Protection Act (TCPA) allows consumers to put themselves on a do-not-call registry. If a number is on the registry, commercial telemarketers are not allowed to call you. Do you believe this has affected the ability of surveyors to obtain accurate polling results? If so, how?

Data Collection
Bias in Sampling
Kimberly Waterbury

Design of Experiments

11 Practice Problems
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00:30
Statistics Informed Decisions Using Data

What is the role of randomization in a designed experiment? If you were conducting a completely randomized design with three treatments and 90 experimental units, describe how you would randomly assign the experimental units to the treatments.

Data Collection
The Design of Experiments
Hossam Mohamed
01:02
Statistics Informed Decisions Using Data

Discuss how a randomized block design is similar to a stratified random sample. What is the purpose of blocking?

Data Collection
The Design of Experiments
Hossam Mohamed
01:27
Statistics Informed Decisions Using Data

Suppose you want to perform an experiment whose goal is to determine whether people prefer Coke or Pepsi. Design an experiment that utilizes the completely randomized design. Design an experiment that utilizes the matched-pairs design. In both designs, be sure to identify the response variable, the role of blinding, and randomization. Which design do you prefer? Why?

Data Collection
The Design of Experiments
Hossam Mohamed

Graphical Representation

17 Practice Problems
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01:33
Statistics Informed Decisions Using Data

The cover of the Ithaca Times from December $7,2000,$ is shown.
(a) Identify the two variables being graphed and describe them in terms of type and measurement level.
(b) What type of data collection method was likely used to create this graph?
(c) What type of graph is displayed?
(d) What message does the graph convey to you? How might this graph be misleading?
(e) Describe at least three things that are wrong with the graph.

Organizing and Summarizing Data
Graphical Misrepresentations of Data
Hossam Mohamed
01:22
Statistics Informed Decisions Using Data

The average per gallon price for regular unleaded gasoline in the United States rose from $\$ 1.46$ in 2001 to $\$ 3.83$ in
2011. Source: U.S. Energy Information Administration
(a) Construct a graphic that is not misleading to depict this situation.
(b) Construct a misleading graphic that makes it appear the average price roughly quadrupled between 2001 and 2011 .

Organizing and Summarizing Data
Graphical Misrepresentations of Data
Hossam Mohamed
00:51
Statistics Informed Decisions Using Data

Organization conducts an annual poll in which it asks a random sample of U.S. adults "How would you rate the overall state of moral values in this country today: excellent, good, only fair, or poor?" The following table represents the percentage of respondents who believe the state of moral values is poor.
(a) Construct a misleading time-series plot that indicates the proportion of U.S. adults who believe that the state of moral values is poor is rapidly increasing.
(b) Construct a time-series plot that is not misleading.

Organizing and Summarizing Data
Graphical Misrepresentations of Data
Hossam Mohamed

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