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Chapter 18: Problem 3

Sampling Shoppers. A reporter for a local television station visits the city's new upscale shopping mall the day before Christmas to interview shoppers. He questions the first 25 shoppers he meets outside one of department stores at the mall. He asks them whether their overall feelings about Christmas shopping are positive, neutral, or negative. Suggest some reasons why it may be risky to act as if the first 25 shoppers at this particular location are an SRS of all shoppers in the city.

Short Answer

Expert verified
The sample may not be representative due to location, time, and diversity biases.

Step by step solution

01

Understanding the Problem

We have a scenario where 25 shoppers at a mall are interviewed about their Christmas shopping experience. The task is to determine why these 25 shoppers might not represent a Simple Random Sample (SRS) of all shoppers in the city.
02

Identifying Location Bias

The shoppers were interviewed at a specific location within the mall, which could affect their responses. This particular department store may attract a specific type of shopper, thus introducing location bias.
03

Considering Time and Date Bias

The interviews are conducted the day before Christmas, which can introduce bias. Shoppers who visit the mall this late might have different shopping behaviors or stress levels compared to those who completed their shopping earlier.
04

Noting Psychological Factors

Shoppers' responses might be influenced by their mood this close to the holiday, potentially skewing the positivity or negativity of their responses.
05

Analyzing Population Diversity

Only 25 individuals are sampled, which is a small fraction of the city's shopper population. This sample might not capture the diversity of economic statuses, ages, and preferences.

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Key Concepts

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

Simple Random Sample (SRS)
In statistics, a Simple Random Sample (SRS) is an essential concept and a method used to eliminate bias while selecting a sample. It ensures each individual in a population has an equal probability of being chosen. This randomness helps in making the sample representative of the entire population. In the given exercise, the selection of the 25 shoppers is not an SRS because they were simply the first people encountered.

To achieve an SRS, you might consider:
  • Using a random number generator to select individuals from a list of all mall shoppers, if such a list exists.
  • Ensuring all areas and times within the mall are equally represented, not just focusing on one location outside a department store.
  • Considering shoppers across different days and times to avoid situational biases.
This approach would help capture a more accurate representation of the shopping attitudes of the city鈥檚 entire population.
Location Bias
Location bias occurs when the selection process favors a particular location, which in turn attracts a specific group of people. In the exercise scenario, the reporter interviews shoppers outside a particular department store. This choice can skew the results because certain stores cater to specific demographics or consumer behaviors.

For instance:
  • High-end department stores might attract shoppers from higher income brackets, leading to underrepresentation of other economic groups.
  • Stores specializing in certain products might bring in shoppers with specific interests, neglecting those who shop elsewhere.
Addressing location bias means varying the locations where interviews take place to include diverse shopping areas within and outside the mall. This helps ensure a balanced representation of all shopping behaviors and attitudes.
Population Diversity
Population diversity refers to the range of different individuals in a population, which includes variations in age, ethnicity, income, and lifestyle. In the exercise, interviewing only 25 people is insufficient to capture the complete diversity of the city's shoppers.

Why is diversity important?
  • Diverse samples provide insights into varied consumer perspectives, revealing broader shopping habits and preferences.
  • Failing to sample widely can lead to misleading conclusions, as the views of underrepresented groups might significantly differ from the sample.
To better reflect population diversity, the sample should cover a wide array of individuals representing the city's overall demographic makeup, ensuring no group is over- or underrepresented.
Time and Date Bias
Time and date bias can greatly influence the data collected during sampling. In the exercise, the interviews were conducted on the day before Christmas. This timing is critical because:
  • Shoppers during the pre-Christmas rush might be more stressed or hurried, affecting their responses.
  • Those shopping earlier might have more relaxed and positive experiences.

Conducting interviews at various times and days would mitigate this type of bias. For instance, gathering data throughout the holiday season, including early December, would provide a broader picture of shopper sentiments. A balanced approach here ensures that the sample captures different shopping moods and behaviors, leading to a more reliable analysis of purchasing attitudes.

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