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Chapter 7: Problem 34

Data from a poll of working women conducted in 2016 by Gallup led to the following estimates: Approximately \(48 \%\) of working women are actively looking for a different job and \(60 \%\) of working women rate greater work- life balance and well-being as a very important attribute in a new job ("Women in America: Work and a Life-Well Lived," www .gallup.com, retrieved November 8,2016 ). a. What additional information about the survey would you need in order to decide if it is reasonable to generalize these estimates to the population of all American adult working women? b. Assuming that the given estimates were based on a representative sample, do you think that the estimates would more likely be closer to the actual population values if the sample size had been 1000 or if the sample size had been 2000 ? Explain.

Short Answer

Expert verified
To determine if it is reasonable to generalize the poll estimates to all American adult working women, we would need additional information on sample size, sampling method, response rate, geographic distribution, demographic diversity, and data quality. With a larger and representative sample size, the estimates would more likely be closer to the actual population values. In this case, a sample size of 2000 would generally lead to more precise estimates compared to a sample size of 1000.

Step by step solution

01

a. Identifying Additional Information Required

To determine if it is reasonable to generalize these estimates to the population of all American adult working women, we would need the following additional information: 1. Sample size: How large was the sample of women surveyed? A larger sample size would increase the likelihood that the estimates are representative of the entire population. 2. Sampling method: How were the women selected for the survey? Was it a random sampling, a stratified sampling, or another method? A well-conducted sampling method increases the chance that the results can be generalized to the entire population. 3. Response rate: What was the response rate for the survey? A higher response rate would mean that the results are more likely to be representative of the population. 4. Geographic distribution: Were women from all regions of the U.S. included in the survey, or were they mainly from specific regions? A broader geographic distribution would make the estimates more applicable to the entire population. 5. Demographic diversity: Were women of all ages, races, income levels, and education levels included in the survey? Ensuring a diverse sample would make the estimates more applicable to the entire population. 6. Data quality: Were there any issues, such as non-response bias or measurement error, that may have affected the survey results? If so, the estimates may not be generalizable to the entire population.
02

b. Comparing Sample Sizes: 1000 vs. 2000

Assuming that the given estimates were based on a representative sample, we can determine if a sample size of 1000 or 2000 would give us more accurate estimates by considering the concept of sampling error. Sampling error is the difference between an estimate calculated from a sample and the true population parameters. As the sample size increases, the standard error (the variability or uncertainty in estimates) decreases, which can lead to more accurate estimates. In other words, increasing the sample size generally generates more precise estimates of population parameters. So, if the sample size had been increased from 1000 to 2000, assuming a representative sample, the estimates would more likely be closer to the actual population values. This is because increasing the sample size leads to smaller standard errors and, in turn, more reliable estimates.

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Key Concepts

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

Sampling Methods
When collecting data, the method of sampling plays a crucial role in ensuring that the results are fair and unbiased. Sampling methods refer to the technique used to select individuals from the population to participate in a survey. There are several ways to conduct sampling:
  • **Random Sampling:** Every individual in the population has an equal chance of being selected. This method reduces the potential for bias and helps in obtaining a sample that mirrors the overall population.
  • **Stratified Sampling:** The population is divided into subgroups, or strata, that share similar characteristics. A random sample is then taken from each subgroup. This method ensures representation across key demographics, like age or income.
  • **Convenience Sampling:** Participants are selected based on their easy availability. While this is less costly, it often does not represent the population well.
Understanding the sampling method is vital, as a well-implemented strategy increases the likelihood that survey results can be generalized to the whole population.
Sample Size
Sample size is the number of participants included in a survey. It greatly influences the reliability of the survey's estimates. The larger the sample size, the more robust and reliable the data becomes. Here鈥檚 why sample size matters:
  • **Accuracy:** Larger samples provide a more precise reflection of the population characteristics. They reduce the effects of unusual data points or outliers.
  • **Margin of Error:** This is the range within which the true population parameter is expected to fall. Larger sample sizes tend to have smaller margins of error, leading to more confidence in the survey results.
  • **Cost vs Benefit:** Bigger samples are often more costly to handle, but they provide more reliable data. It鈥檚 crucial to find the right balance between cost and the level of precision required.
Sample size is a cornerstone of statistical analysis, and a well-calculated sample size will lead to more credible survey outcomes.
Survey Generalization
Survey generalization is the ability to apply the results from a sample to the broader population. When a survey is generalized well, it means that the findings can be expected to reflect the reality for the entire population. Several factors impact survey generalization:
  • **Representativeness:** The sample must adequately reflect the population in aspects like demographics and geography.
  • **Sample Size:** A sufficient number of respondents helps ensure results reflect the population.
  • **Sampling Method:** A random and unbiased method improves the generalizability of findings.
If all these factors align well with the population demographics, the survey results can be accurately extended beyond the sample.
Data Quality
High data quality in surveys ensures that the collected information is accurate, reliable, and valid for analysis. Several elements contribute to ultimate data quality:
  • **Design of Survey Questions:** Clear, unbiased questions ensure that responses accurately represent participant opinions.
  • **Response Accuracy:** Ensures that the data collected are truthful and consistent with participants鈥� real beliefs or behaviors.
  • **Handling Bias:** Identifying and correcting biases such as non-response or sampling bias ensures quality.
Attention to data quality should be a priority to ensure that survey results are trustworthy and meaningful.
Response Rate
The response rate is the percentage of people who completed the survey out of all those who were invited to participate. It鈥檚 a crucial factor indicating the representativeness of the survey data:
  • **High Response Rates:** These generally suggest better data quality and more reliable, generalized results. They indicate that the views of those who responded are representative of the entire population.
  • **Factors Affecting Rate:** Survey length, communication, and motivation can impact whether people choose to respond.
  • **Improving Response Rates:** Offering incentives, follow-ups, and simplifying the survey can help increase response rates.
A robust response rate supports strong and valid survey findings, reinforcing the data's credibility.

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Most popular questions from this chapter

In a study of whether taking a garlic supplement reduces the risk of getting a cold, 146 participants were randomly assigned to either a garlic supplement group or to a group that did not take a garlic supplement ("Garlic for the Common Cold," Cochrane Database of Systematic Reviews, 2009). Based on the study, it was concluded that the proportion of people taking a garlic supplement who get a cold is lower than the proportion of those not taking a garlic supplement who get a cold. a. What claim about the effect of taking garlic is supported by the data from this study? b. Is it possible that the conclusion that the proportion of people taking garlic who get a cold is lower than the proportion for those not taking garlic is incorrect? Explain. c. If the number of people participating in the study had been \(50,\) do you think that the chance of an incorrect conclusion would be greater than, about the same as, or lower than for the study described?

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