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Chapter 7: Problem 2

In 2017 Pew Research Center polled 3930 adults in the United States and found that \(43 \%\) reported playing video games often on some kind of electronic device. a. Identify the population and the sample. b. What is the parameter of interest? What is the statistic?

Short Answer

Expert verified
The population is all adults in the United States. The sample consists of the 3930 adults who were polled. The parameter of interest is the proportion of adults in the U.S playing video games often. The statistic is the \(43 \%\) of the polled adults who reported playing video games often.

Step by step solution

01

Identifying the population

The population refers to the whole group that an observation is being made on. In this case, the population is all adults in the United States.
02

Identifying the sample

The sample refers to a part of the population that is chosen for the observation. In the case of the exercise, the sample is the 3930 adults that Pew Research Center polled.
03

Identifying the parameter of interest

The parameter of interest is the characteristic of the population that the research is interested in. Here, it is the proportion of adults in the U.S that report playing video games often on some kind of electronic device.
04

Identifying the statistic

The statistic is an estimate of the parameter that is calculated from the sample. In this exercise, the statistic is the \(43 \%\) of the polled adults who reported playing video games often.

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Key Concepts

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

Population and Sample
When it comes to research in statistics, it is crucial to distinguish between the 'population' and the 'sample.' Imagine a large fish tank filled with various fish species - that's your population, the entire group that you're interested in studying. However, it's not always practical or possible to examine every single fish in the tank. So, what do we do? We net a smaller, manageable group of fish - this smaller group we captured is our 'sample.'

In the example given, the population would be all adults in the United States. Think of it as the 'big picture' we鈥檙e trying to understand. The sample, on the other hand, is the 3930 adults surveyed by the Pew Research Center. This distinction is vital because the sample needs to accurately reflect the population for the conclusions drawn to be reliable. If we only captured goldfish, but wanted to make statements about all fish in the tank, our results wouldn't be valid!
Parameter of Interest
Next up is the 'parameter of interest.' It's the specific characteristic we're trying to measure within the population. If our fish tank represents all adults in the United States, and we want to know what proportion enjoys a particular type of fish food, that proportion is our parameter of interest.

Using our exercise, the parameter of interest is the percentage of all adults in the U.S. who play video games often on an electronic device. It鈥檚 like asking, 'How many of the fish in this entire tank prefer this flaky food over pellets?' We鈥檙e focused on this one characteristic and trying to measure it accurately for the whole tank (population), but through our sample.
Statistic in Research
Finally, let's dive into the 'statistic in research.' After netting some fish and observing what food they prefer, we can then make an estimate about the entire tank. This estimate is the statistic. It's derived from our sample and can tell us a lot about our population, even though we haven't observed every single fish.

In the context of our exercise, the reported 43 percent of the sampled adults playing video games often is the statistic. It鈥檚 like saying, 'Based on the fish we caught and observed, we estimate that about 43 percent of the entire fish tank loves flaky food.' The statistic is a snapshot from our sample that provides an insight into the larger population's behavior, ensuring that we can make informed statements without having to survey each individual.

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Most popular questions from this chapter

Two symbols are used for the standard deviation: \(\sigma\) and s. a. Which represents a parameter, and which represents a statistic? b. To estimate the commute time for all students at a college, 100 students are asked to report their commute times in minutes. The standard deviation for these 100 commute times was \(13.9\) minutes. Is this standard deviation \(\sigma\) or s?

A recent Monmouth University poll found that 675 out of 1008 randomly selected people in the United States felt that college and universities with big sports programs placed too much emphasis on athletics over academics. Assuming the conditions for using the CLT were met, use the Minitab output provided to answer these questions. $$ \begin{aligned} &\text { Descriptive Statistics }\\\ &\begin{array}{rrrr} \mathrm{N} & \text { Event } & \text { Sample } \mathrm{p} & 95 \% \mathrm{Cl} \text { for } \mathrm{p} \\ \hline 1008 & 675 & 0.669643 & (0.639648,0.698643) \end{array} \end{aligned} $$ a. Complete this sentence: I am \(95 \%\) confident that the population proportion believing that colleges and universities with big sports programs place too much emphasis on athletics over academics is between _____ and _____. Report each number as a percentage rounded to one decimal place. b. Suppose a sports blogger wrote an article claiming that the majority of Americans believe that colleges and university with big sports programs place too much emphasis on athletics over academics. Does this confidence interval support the blogger's claim? Explain your reasoning.

According to a Gallup poll, \(45 \%\) of Americans actively seek out organic foods when shopping. Suppose a random sample of 500 Americans is selected and the proportion who actively seek out organic foods is recorded. a. What value should we expect for the sample proportion? b. What is the standard error? c. Use your answers to parts a and b to complete this sentence: We expect _____% of Americans to actively seek out organic foods when shopping, give or take _____%. d. Would it be surprising to find a sample proportion of \(55 \% ?\) Why or why not? e. What effect would decreasing the sample size from 500 to 100 have on the standard error?

Chapman University conducts an annual Survey of American Fears. One of the objectives of this survey is to collect annual data on the fears, worries, and concerns of Americans. In 2017 the survey sampled 1207 participants. One of the survey findings was that \(16 \%\) believe that Bigfoot is a real creature. Identify the sample and population. Is the value \(16 \%\) a parameter or a statistic? What symbol would be use for this value?

In 2003 and 2017 Gallup asked Democratic voters about their views on the FBI. In \(2003,44 \%\) thought the FBI did a good or excellent job. In \(2017,69 \%\) of Democratic voters felt this way. Assume these percentages are based on samples of 1200 Democratic voters. a. Can we conclude, on the basis of these two percentages alone, that the proportion of Democratic voters who think the FBI is doing a good or excellent job has increase from 2003 to \(2017 ?\) Why or why not? b. Check that the conditions for using a two-proportion confidence interval hold. You can assume that the sample is a random sample. c. Construct a \(95 \%\) confidence interval for the difference in the proportions of Democratic voters who believe the FBI is doing a good or excellent job, \(p_{1}-p_{2}\). Let \(p_{1}\) be the proportion of Democratic voters who felt this way in 2003 and \(p_{2}\) be the proportion of Democratic voters who felt this way in 2017 . d. Interpret the interval you constructed in part c. Has the proportion of Democratic voters who feel this way increased? Explain.
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