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Chapter 7: Problem 102

Maria opposes capital punishment and wants to find out if a majority of voters in her state support it. She goes to a church picnic and asks everyone there for their opinion. Because most of them oppose capital punishment, she concludes that a vote in her state would go against it. Explain what is wrong with Maria's approach.

Short Answer

Expert verified
The problem with Maria's approach is that the sample of people from the church picnic is likely not representative of all voters in her state. Therefore, this could lead to sampling bias, resulting in incorrect conclusions about the majority view on capital punishment.

Step by step solution

01

Identify the Sample and Population

Maria's sample is the individuals at the church picnic whom she asked for their opinion about capital punishment. The population is the voters in her state.
02

Understand the Sampling Method

Maria collected her sample by asking people at a church picnic. Therefore, her method can be classified as convenience sampling because she collected data from people who were easily available to her.
03

Evaluate the Sample Representativeness

The sample Maria used might not be representative of the entire population. People at a church picnic might have common characteristics that make them more likely to oppose capital punishment. For example, they might share similar religious beliefs that guide their views on moral issues like capital punishment.
04

Identify the Bias

Because the sample is not likely to be representative of the population, the conclusion drawn from it may be biased. This bias is known as selection bias or sampling bias because the method of selection led to a sample that does not accurately reflect the population.
05

Explain the Problem with the Conclusion

Maria's conclusion might be incorrect because it is based on data from a biased sample. She can't infer the opinion of all voters in her state on capital punishment based on the opinion of the people at the church picnic, as they do not represent the broader population of voters in her state.

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Most popular questions from this chapter

Assume your class has 30 students and you want a random sample of 10 of them. A student suggests asking each student to flip a coin, and if the coin comes up heads, then he or she is in your sample. Explain why this is not a good method.

a. If a rifleman's gunsight is adjusted incorrectly, he might shoot bullets consistently close to 2 feet left of the bull's-eye target. Draw a sketch of the target with the bullet holes. Does this show lack of precision or bias? b. Draw a second sketch of the target if the shots are both unbiased and precise (have little variation). The rifleman's aim is not perfect, so your sketches should show more than one bullet hole.

From Formula \(7.2\), an estimate for margin of error for a \(95 \%\) confidence interval is \(m=2 \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\) where \(\mathrm{n}\) is the required sample size and \(\hat{p}\) is the sample proportion. Since we do not know a value for \(\hat{p}\), we use a conservative estimate of \(0.50\) for \(\hat{p}\). Replace \(\hat{p}\) with \(0.50\) in the formula and simplify.

Is simple random sampling usually done with or without replacement?

Suppose it is known that \(60 \%\) of employees at a company use a Flexible Spending Account (FSA) benefit. a. If a random sample of 200 employees is selected, do we expect that exactly \(60 \%\) of the sample uses an FSA? Why or why not? b. Find the standard error for samples of size 200 drawn from this population. What adjustments could be made to the sampling method to produce a sample proportion that is more precise?
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