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Florida Voters. Florida played a key role in recent presidential elections. Voter registration records in August 2016 show that \(38 \%\) of Florida voters are registered as Democrats and \(36 \%\) as Republicans. (Most of the others did not choose a party.) In September 2016 you wsed a random digit dialing device to poll voters for the 2016 presidential elections. You used it to call 250 randomly chosen residential telephones in Florida. Of the registered voters contacted, \(35 \%\) are registered Democrats. Is each of the boldface numbers a parameter or a statistic?

Short Answer

Expert verified
Parameter: 38% and 36%; Statistic: 35%.

Step by step solution

01

Understanding Parameters and Statistics

A **parameter** describes a characteristic of an entire population, whereas a **statistic** describes a characteristic of a sample from the population. In this problem, we need to determine which numbers describe the entire population of Florida voters and which describe a sample taken from that population.
02

Identify Parameters

Parameters are values that come from the whole population. In the problem, the first two percentages given are about the entire population of Florida voters: \(38\%\) of voters are registered as Democrats, and \(36\%\) are registered as Republicans. These two percentages are parameters because they describe the entire population of registered voters in Florida.
03

Identify Statistics

Statistics are values calculated from a sample of the population. In this problem, the percentage given from the poll (\(35\%\) of registered voters contacted are Democrats) comes from a sample of 250 telephones. This number is a statistic because it describes a sample proportion of registered Democrats from those contacted by phone polling.

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Key Concepts

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

Parameter vs Statistic
In the world of statistics, understanding the distinction between a parameter and a statistic is essential. A **parameter** is a numerical characteristic that describes an entire population. Think of it as a complete summary of some aspect of every member in the group you're interested in. For instance, if we're looking at all Florida voters, a parameter like "38% are registered as Democrats" gives us a snapshot of all registered voters across the state.

On the other hand, a **statistic** is a number that describes a characteristic of a sample taken from that population. It provides an estimate based on a smaller group, rather than the entire population. For example, when a poll conducted over the phone found that "35% of the voters contacted are Democrats," this is a statistic. It represents only the opinions or characteristics of those 250 individuals sampled, not the whole population of Florida voters, hence why the distinction is crucial in interpreting data correctly.
Population vs Sample
Understanding the difference between a population and a sample is fundamental in statistics. A **population** includes every subject or item that falls under the criteria we are studying. In our example, the population would be all registered voters in Florida. This comprehensive group is what we aim to understand and make generalizations about.

Conversely, a **sample** is a subset of that population, ideally selected in a way that it represents the larger group. The poll of 250 voters created a sample from the Florida voter population. By analyzing this smaller group, statisticians aim to infer insights about the population at large. However, because we only have data from the sample in such exercises, the insights can carry a margin of error, reflecting how well the sample represents the whole.
Voter Registration Data Analysis
Analyzing voter registration data involves carefully studying how data is collected, categorized, and interpreted to make informed decisions. The data in reference provides insights into how Florida voters are registered by political party – with 38% registered as Democrats and 36% as Republicans as of August 2016. These figures are essential for understanding the broader voting landscape and predicting election outcomes.

When conducting a poll, like dialing 250 random phone numbers, the aim is often to gather a snapshot of public opinion or voter registration distribution. However, the result (35% of the polled voters identifying as Democrats) highlights the importance of understanding both data collection and analysis nuances. It's crucial to acknowledge that such a result might differ from the population's actual registration figures due to sample selection and random variability.
  • Consider how seasonal trends or recent events may influence voter registration patterns.
  • Evaluate if the sample is representative of the overall voter demographic, considering factors such as geographic distribution and voter engagement.
These considerations ensure a precise and honest interpretation of voter trends that can inform decision-making in political campaigns and policy assessments.

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Most popular questions from this chapter

The number of hours a battery lasts before failing varies from battery to battery. The distribution of failure times follows an exponential distribution (see Example \(15.7\) ), which is strongly skewed to the right. The central limit theorem says that (a) as we look at more and more batteries, their average failure time gets ever closer to the mean \(\mu\) for all batteries of this type. (b) the average failure time of a large number of batteries has a distribution of the same shape (strongly skewed) as the distribution for individual batteries. (c) the average failure time of a large number of batteries has a distribution that is close to Normal.

Pollutants in auto exhausts, continued. The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life \((150,000\) miles of driving) of cars of a particular model varies Normally with mean \(80 \mathrm{mg} / \mathrm{mi}\) and standard deviation \(4 \mathrm{mg} / \mathrm{mi}\). A company has 25 cars of this model in its fleet. What is the level \(L\) such that the probability that the average \(\mathrm{NOX}+\mathrm{NMOG}\) level \(\mathrm{x}^{-} 1\) for the fleet is greater than \(L\) is only \(0.01\) ? (Hint: This requires a backward Normal calculation. See page 91 in Chapter 3 if you need to review.)

Sampling students. To estimate the mean score of those who took the Medical College Admission Test on your campes, you will obtain the scores of an SRS of students. From published information, you know that the scores are approximately Normal with standard deviation about 10.4. How large an SRS must you take to reduce the standard deviation of the sample mean score to 1 ?

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for six randomly chosen women exceeds 270 days is about (a) \(0.40 .\) (b) \(0.27\) (c) \(0.07\)

Sampling Distribution versus Population Distribution. The 2015 American Time Use Survey contains data on how many minutes of sleep per night each of 10,900 survey participants estimated they get. 3 The times follow the Normal distribution with mean \(529.9\) minutes and standard deviation \(135.6\) minutes. An SRS of 100 of the participants has a mean time of \(x^{-}=514.4 \bar{x}=514.4\) minutes. A second SRS of size 100 has mean \(x^{-}=539.3 r=539.3\) minutes. After many SRSs, the many values of the sample mean \(x^{-} x\) follow the Normal distribution with mean \(529.9\) minutes and standard deviation \(13.56\) minutes. (a) What is the population? What values does the population distribution describe? What is this distribution? (b) What values does the sampling distribution of \(x^{-} x\) describe? What is the sampling distribution?

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