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Chapter 7: Problem 28

Suppose you attend a school that offers both traditional courses and online courses. You want to know the average age of all the students. You walk around campus asking those students that you meet how old they are. Would this result in an unbiased sample?

Short Answer

Expert verified
No, the sample would be biased. It only includes the ages of students who are on campus at that time and willing to answer the question, potentially excluding online students and other students not on campus at that time.

Step by step solution

01

Understanding the definition of an Unbiased Sample

It's important to understand that in the context of statistics, an unbiased sample is a set of observations chosen randomly without any favor or prejudice, giving it high representativeness of the overall population. Each member of the population should have an equally likely chance to be part of the sample.
02

Evaluating the given Scenario

Now let's evaluate this case. In the scenario where you walk around campus asking students about their ages, it's clear that the method of selecting the sample is not random. It's confined to students who are available on the campus at that time and who are willing to participate in the survey.
03

Determining if the Sample is Biased or Unbiased

Given that online students and possibly some traditional courses students who aren't on the campus at that time aren't included, it's evident that there's a bias in the sample selection. Thus, the sample obtained through this method wouldn't be an unbiased sample.

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Most popular questions from this chapter

The Gallup poll reported that \(45 \%\) of Americans have tried marijuana. This was based on a survey of 1021 Americans and had a margin of error of plus or minus 5 percentage points with a \(95 \%\) level of confidence. a. State the survey results in confidence interval form and interpret the interval. b. If the Gallup Poll was to conduct 100 such surveys of 1021 Americans, how many of them would result in confidence intervals that did not include the true population proportion? c. Suppose a student wrote this interpretation of the interval: "We are \(95 \%\) confident that the percentage of Americans who have tried marijuana is between \(40 \%\) and \(50 \%\)." What, if anything, is incorrect in this interpretation?

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?

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.

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. $$\begin{aligned}&\text { Descriptive Statistics }\\\&\begin{array}{rrrr}\mathrm{N} & \text { Event } & \text { Sample p } & 95 \% \mathrm{Cl} \text { for } \mathrm{p} \\\\\hline 1008 & 675 & 0.669643 & (0.639648,0.698643)\end{array}\end{aligned}$$ 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.

Just the Boys Refer to Exercise \(7.77\) for information. This data set records results just for the boys. $$\begin{array}{|lcc|}\hline & \text { Preschool } & \text { No Preschool } \\\\\hline \text { Grad HS } & 16 & 21 \\\\\hline \text { No Grad HS } & 16 & 18 \\\\\hline\end{array}$$ a. Find and compare the percentages that graduated for each group, descriptively. Does this suggest that preschool was linked with a higher graduation rate? b. Verify that the conditions for a two-proportion confidence interval are satisfied. c. Indicate which one of the following statements is correct. i. The interval does not capture 0 , suggesting that it is plausible that the proportions are the same. ii. The interval does not capture 0 , suggesting that it is not plausible that the proportions are the same. iii. The interval captures 0 , suggesting that it is plausible that the population proportions are the same. iv. The interval captures 0 , suggesting that it is not plausible that the population proportions are the same. d. Would a \(99 \%\) confidence interval be wider or narrower?
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