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Chapter 7: Q.24 (page 431)

Increasing the sample size of an opinion poll will

(a) reduce the bias of the poll result.

(b) reduce the variability of the poll result.

(c) reduce the effect of nonresponse on the poll.

(d) reduce the variability of opinions.

(e) all of the above.

Short Answer

Expert verified

A correct answer is an option (b) to reduce the variability of opinions.

Step by step solution

01

Given Information

Increasing the sample size of an opinion poll.

02

Explanation

A larger sample size results in more information about the population and thus better estimates of the population.

If we have better estimates of the population, then we also know that there is less variability.

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Most popular questions from this chapter

Your mail-order company advertises that it ships 90%of its orders within three working days. You select an SRS of 100of the 5000orders received in the past week for an audit. The audit reveals that 86of these orders were shipped on time.

(a) If the company really ships 90%of its orders on time, what is the probability that the proportion in an SRS of 100orders is as small as the proportion in your sample or smaller? Follow the four-step process.

(b) A critic says, 鈥淎ha! You claim 90%, but in your sample, the on-time percentage is lower than that. So the 90%claim is wrong.鈥� Explain in simple language why your probability calculation in (a) shows that the result of the sample does not refute the 90%claim.

A newborn baby has extremely low birth weight (ELBW) if it weighs less than 1000 grams. A study of the health of such children in later years examined a random sample of 219 children. Their mean weight at birth was x炉=810 grams. This sample mean is an unbiased estimator of the mean weight渭 in the population of all ELBW babies, which means that

(a) in all possible samples of size 219 from this population, the mean of the values of x炉 will equal 810 .

(b) in all possible samples of size 219 from this population, the mean of the values of x炉 will equal 渭.

(c) as we take larger and larger samples from this population, x炉 will get closer and closer to 渭.

(d) in all possible samples of size 219 from this population, the values of x炉 will have a distribution that is close to Normal.

(e) the person measuring the children's weights does so without any systematic error.

Tall girls According to the National Center for Health Statistics, the distribution of heights for 16-year-old females is modeled well by a Normal density curve with mean 渭=64inches and standard deviation 蟽=2.5inches. To see if this distribution applies at their high school, an AP Statistics class takes an SRS of 20of the 30016-year-old females at the school and measures their heights. What values of the sample mean x would be consistent with the population distribution being N(64,2.5)? To find out, we used Fathom software to simulate choosing 250SRSs of size n=20students from a population that is N(64,2.5). The figure below is a dotplot of the sample mean height x of the students in the sample.

(a) Is this the sampling distribution of x? Justify your answer.

(b) Describe the distribution. Are there any obvious outliers?

(c) Suppose that the average height of the 20girls in the class鈥檚 actual sample is x=64.7. What would you conclude about the population mean height Mfor the 16-year-old females at the school? Explain.

AP2.24. Every 17years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, and then die. (There are several different 鈥渂roods,鈥� so we experience cicada eruptions more often than every 17years.) There are so many cicadas that their dead bodies can serve as fertilizer and increase plant growth. In a study, a researcher added 10cicadas under 39randomly selected plants in a natural plot of American bell flowers on the forest floor, leaving other plants undisturbed. One of the response variables measured was the size of seeds produced by the plants. Here are the box plots and summary statistics of seed mass (in milligrams) for 39cicada plants and 33undisturbed (control) plants:

Variable: n Minimum Q1 Median Q3 Maximum

Cicada plants: 39 0.17 0.22 0.25 0.28 0.35
Control plants: 33 0.14 0.19 0.25 0.26 0.29
(a) Is this an observational study or an experiment? Explain.
(b) Based on the graphical displays, which distribution has
the larger mean? Justify your answer.
(c) Do the data support the idea that dead cicadas can
serve as fertilizer? Give graphical and numerical evidence
to support your conclusion.

According to the U.S. census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100adults in a certain section of the county found that65 owned their home. Which one
of the following represents the approximate probability of obtaining a sample of 100adults in which fewer than 65own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

(a) 10065(0.71)65(0.29)35

(b) 10065(0.29)65(0.71)35
(c) Pz<0.65-0.71(0.71)(0.29)100

(d) Pz<0.65-0.71(0.65)(0.35)100
(e) Pz<0.65-0.71(0.71)(0.29)100
See all solutions

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