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91Ó°ÊÓ

A questionnaire was mailed to 1000 registered municipal voters selected at random. Only 500 questionnaires were returned, and of the 500 returned, 360 respondents were strongly opposed to a surcharge proposed to support the city Parks and Recreation Department. Are you willing to accept the \(72 \%\) figure as a valid estimate of the percentage in the city who are opposed to the surcharge? Why or why not?

Short Answer

Expert verified
Provide reasoning for your answer. Answer: Given the 50% response rate and the potential for biases, such as non-response bias and selection bias, the sample might not be fully representative of the population views. As a result, it might not be appropriate to consider the 72% figure as a valid estimate of the percentage of municipal voters in the city who are opposed to the surcharge. Further analysis or additional data collection methods may be needed to derive a more accurate estimate.

Step by step solution

01

Calculate the response rate

The response rate is calculated by dividing the number of questionnaires returned (500) by the total number of questionnaires mailed out (1000). Response Rate = \(\frac{500}{1000}\) = 0.5 or 50%
02

Evaluate the sample size

A sample size of 500 respondents can be considered as a reasonably large sample size. However, it is crucial to take into consideration the response rate, which in this case is 50%, making the sample less representative.
03

Assess potential biases in the sample

There could have been several biases involved, such as: 1. Non-response bias: Individuals who are strongly opinionated about the surcharge might be more likely to respond to the survey than individuals with less strong opinions. 2. Selection bias: The survey was sent to registered municipal voters only, which disregards the opinions of non-registered citizens.
04

Determine if the percentage can be considered valid

Given the 50% response rate and the potential for biases, the sample might not be fully representative of the population views; thus, it might not be appropriate to accept the 72% figure as a valid estimate of the percentage in the city who are opposed to the surcharge. Further analysis or additional data collection methods may be needed to derive a more accurate estimate.

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Key Concepts

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

Response Rate in Surveys
Understanding the response rate in surveys is crucial when assessing the quality of survey results. The response rate, essentially, is the portion of individuals who return the survey out of those who received it. High response rates often indicate that the results may be more representative of the target population. On the other hand, a low response rate, such as the 50% seen in the mentioned exercise, can raise concerns about the representativeness of the data.

For instance, if those who feel strongly about an issue are more likely to respond, this could result in non-response bias. To enhance response rates, researchers might implement follow-up contacts, simplify survey completion, or even offer incentives. However, it is not only the sheer number that matters; the characteristics of the non-respondents are equally important to consider in evaluating the potential impact on survey results. Always aim for a high response rate, but also be prepared to assess and address the implications of the response rate on your survey's findings.
Sample Size Assessment
Assessing sample size is a key step in conducting surveys. It strikes a balance between statistical confidence and practical constraints such as TIME and resources. In the context of this exercise, a sample size of 500 out of 1000 might appear robust, but it's essential to consider the response rate in evaluating its adequacy.

Larger sample sizes generally provide more precise estimates of the population characteristics and reduce the margin of error in the results. Nonetheless, it's not just about having a large sample size; the sample also needs to be representative of the entire population. A representative sample ensures that every segment of the population is proportionately included, which strengthens the validity of the survey findings. Techniques such as stratified sampling or oversampling can be employed to ensure representativeness, especially when dealing with diverse populations.
Survey Bias Types
Survey bias can significantly distort the outcomes of research, leading to invalid conclusions. There are various types of survey bias to be vigilant about.

The first is non-response bias, which arises when individuals who do not participate in the survey differ in significant ways from those who do. To mitigate this, researchers can increase efforts to reach non-respondents or use weighting techniques to adjust for the differences.

Another common bias is selection bias, mentioned in the original exercise. It happens when the sample is not randomly selected or does not adequately represent the population. Ensuring random selection and inclusive criteria can help prevent this bias.

Also noteworthy is measurement bias, which occurs when the questions are leading or misinterpreted by respondents. Clear and neutral wording can help minimize this risk.

It's also crucial to watch out for confirmation bias, where researchers might unconsciously promote outcomes that confirm their expectations or hypotheses. Maintaining objectivity and employing blind or double-blind study designs can reduce this bias.

Ultimately, recognizing and addressing the various types of bias is fundamental to achieving accurate and trustworthy survey results.

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