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Chapter 1: Problem 6

The increasing popularity of online shopping has many consumers using Internet access at work to browse and shop online. In fact, the Monday after Thanksgiving has been nicknamed "Cyber Monday" because of the large increase in online purchases that occurs on that day. Data from a large-scale survey by a market research firm (Detroit Free Press, November 26,2005 ) was used to compute estimates of the percent of men and women who shop online while at work. The resulting estimates probably won't make most employers happy \(-42 \%\) of the men and \(32 \%\) of the women in the sample were shopping online at work! Are the estimates given computed using data from a sample or for the entire population?

Short Answer

Expert verified
The estimates are calculated based on a sample, not the entire population.

Step by step solution

01

Understanding of Sample and Population

When we discuss statistics, we often talk about a sample or a population. A sample is a subset of a population. In this context, the population would be all men and women who work, while a sample is a subset of these working men and women.
02

Analyse the Statements

Analyse the statements carefully. The statement is 'Data from a large-scale survey by a market research firm was used to compute estimates...' This clearly points out that a market research firm conducted a survey and then estimated percentages. Generally, surveys do not cover the entirety of a population.
03

Conclusion

The estimates are calculated based on a sample of the population. This is because the percentages of men and women shopping online at work is based on a large-scale survey, and not the entire working population.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Statistics and Data Analysis
Understanding statistics is crucial for interpreting data and making informed decisions. The heart of statistics is about examining variables within groups to find patterns, relationships, or discrepancies. In the example of online shopping behavior, data analysis involves extracting meaningful insights, such as the percentage of men and women shopping online while at work, from the collected data.
Statistics reveal trends that could potentially influence strategies for marketing, management, and beyond. For instance, if a high percentage of individuals are shopping online at work, this could indicate a need for companies to reconsider their internet usage policies or it could signal online retailers to target promotions during work hours.
Effective data analysis often requires the use of various statistical techniques such as calculation of averages, standard deviation, correlation coefficients, and hypothesis testing. These methods help in understanding the data more comprehensively and in deciding whether the findings can be generalized to a larger population.
Population Estimation
Population estimation involves deriving the approximate count or characteristics of an entire group (population) based on the analysis of a part of that group (sample). In the context of the exercise, the population would consist of all employed men and women who have the opportunity to shop online while at work. However, it is impractical and often impossible to collect data from every person in this group.
Thus, statisticians use a sample, which is a smaller, manageable portion of the population, to draw inferences. The key is ensuring that the sample represents the population well. Techniques like random sampling help improve representation.
Estimations from a sample need to be treated with a certain level of caution because they are subject to sampling error鈥攖he discrepancy between the sample's characteristics and the true values in the population. Confidence intervals and other statistical measures are used to express the reliability and precision of these estimates.
Sampling Methods
Sampling methods are fundamental to conducting surveys and research. They decide how the participants (samples) are chosen from the population. Common sampling methods include:
  • Random Sampling: Each member of the population has an equal chance of being selected.
  • Stratified Sampling: The population is divided into subgroups (strata) based on certain characteristics, and random samples are taken from each stratum.
  • Cluster Sampling: The population is divided into clusters, often geographically, and a random sample of clusters is studied.
  • Systematic Sampling: Every nth member of the population is chosen after a random starting point.
  • Convenience Sampling: Participants are selected based on their availability or convenience to the researcher, which might not be representative of the entire population.
In our example of online shopping, the type of sampling method used can significantly affect the validity of the results. If the market research firm employed random sampling, the estimate of 42% of men and 32% of women shopping online at work is more likely to reflect the actual behavior of the entire working population. In contrast, if a convenience sampling method was used, results might be biased, thus not accurately representing the population's behavior.

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Most popular questions from this chapter

For the following numerical variables, state whether each is discrete or continuous. a. The length of a 1 -year-old rattlesnake b. The altitude of a location in California selected randomly by throwing a dart at a map of the state c. The distance from the left edge at which a 12 -inch plastic ruler snaps when bent sufficiently to break d. The price per gallon paid by the next customer to buy gas at a particular station

The report "Testing the Waters \(2009^{\prime \prime}\) (www nrdcorg) included information on the water quality at the 82 most popular swimming beaches in California. Thirty-eight of these beaches are in Los Angeles County. For each beach, water quality was tested weekly and the data below are the percent of the tests in 2008 that failed to meet water quality standards. Los Angeles County \(\begin{array}{llllllllll}32 & 4 & 6 & 4 & 4 & 7 & 4 & 27 & 19 & 23\end{array}\) \(\begin{array}{lll}7 & 4 & 27\end{array}\) \(\begin{array}{rrrr}6 & 4 & 4 & 7 \\\ 11 & 19 & 9 & 11\end{array}\) \(\begin{array}{rr}32 & 4 \\ 19 & 13\end{array}\) \(\begin{array}{llllllllll}19 & 13 & 11 & 19 & 9 & 11 & 16 & 23 & 19 & 16\end{array}\) \(\begin{array}{llllllllll}33 & 12 & 29 & 3 & 11 & 6 & 22 & 18 & 31 & 43\end{array}\) \(\begin{array}{llllllll}17 & 26 & 17 & 20 & 10 & 6 & 14 & 11\end{array}\) Other Counties 0 0 0 \(2 \quad 3\) 7 511 \(5 \quad 7\) \(\begin{array}{lllllll}15 & 8 & 1 & 5 & 0 & 5 & 4\end{array}\) 1 0 0 5 \(\begin{array}{lllllll}1 & 0 & 2 & 7 & 0 & 2 & 2\end{array}\) 3 3 \(\begin{array}{lllllllll}0 & 8 & 8 & 8 & 0 & 0 & 17 & 4 & 3\end{array}\) : \(\begin{array}{lll}10 & 40 & 3\end{array}\) a. Construct a dotplot of the percent of tests failing to meet water quality standards for the Los Angeles County beaches. Write a few sentences describing any interesting features of the dotplot. b. Construct a dotplot of the percent of tests failing to meet water quality standards for the beaches in other counties. Write a few sentences describing any interesting features of the dotplot. c. Based on the two dotplots from Parts (a) and (b), describe how the percent of tests that fail to meet water quality standards for beaches in Los Angeles county differs from those of other counties.

For each of the following situations, give a set of possible data values that might arise from making the observations described. a. The manufacturer for each of the next 10 automobiles to pass through a given intersection is noted. b. The grade point average for each of the 15 seniors in a statistics class is determined. c. The number of gas pumps in use at each of 20 gas stations at a particular time is determined. d. The actual net weight of each of 12 bags of fertilizer having a labeled weight of 50 pounds is determined. e. Fifteen different radio stations are monitored during a 1-hour period, and the amount of time devoted to commercials is determined for each.

The article "Brain Shunt Tested to Treat Alzheimer's" (San Francisco Chronicle, October 23 . 2002) summarizes the findings of a study that appeared in the journal Neurology. Doctors at Stanford Medical Center were interested in determining whether a new surgical approach to treating Alzheimer's disease results in improved memory functioning. The surgical procedure involves implanting a thin tube, called a shunt, which is designed to drain toxins from the fluid-filled space that cushions the brain. Eleven patients had shunts implanted and were followed for a year, receiving quarterly tests of memory function. Another sample of Alzheimer's patients was used as a comparison group. Those in the comparison group received the standard care for Alzheimer's disease. After analyzing the data from this study, the investigators concluded that the "results suggested the treated patients essentially held their own in the cognitive tests while the patients in the control group steadily declined. However, the study was too small to produce conclusive statistical evidence." a. What were the researchers trying to learn? What questions motivated their research? b. Do you think that the study was conducted in a reasonable way? What additional information would you want in order to evaluate this study?

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