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Chapter 8: Q. 20 (page 483)

An online poll posed the following question:

It is now possible for school students to log on to Internet sites and download homework. Everything from book reports to doctoral dissertations can be downloaded free or for a fee. Do you believe that giving a student who is caught plagiarizing an F for their assignment is the right punishment?

Of the 20,125people who responded, 14,793clicked 鈥淵es.鈥� That鈥檚 73.5%of the sample. Based on this sample, a 95%confidence interval for the percent of the population who would say 鈥淵es鈥� is 73.5% 卤0.61. Which of the three inference conditions is violated? Why is this confidence interval worthless?

Short Answer

Expert verified

The inference conditions violated are:

Random, Voluntary response sample.

Step by step solution

01

Given Information

Violated inference condition

Three inference conditions: Normal, Independent, Random

The condition of Random was violated, because the sample is collected by an online poll which results in a voluntary response sample and thus not a random sample.

02

Explanation

We should point out that the sample of 20,125people is made up of people who elected to participate, making it a voluntary response sample.

Because persons with the strongest opinions are more likely to engage in voluntary response sampling, the population results are likely to diverge significantly from the sample results.

Because the percentage of 73.5percentage . is not a credible measurement for the population percentage, the confidence interval is unlikely to contain the true value of the population proportion.

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Most popular questions from this chapter

Power lines and cancer (4.2,4.3)Does living near power lines cause leukemia in children? The

National Cancer Institute spent 5 years and $5million gathering data on this question. The researchers compared 638children who had leukemia with620who did not. They went into the homes and actually measured the magnetic fields in children's bedrooms, in other rooms, and at the front door. They recorded facts about power lines near the family home and also near the mother's residence when she was pregnant. Result: no connection between leukemia and exposure to magnetic fields of the kind produced by power lines was found.

(a) Was this an observational study or an experiment? Justify your answer.

(b) Does this study show that living near power lines doesn't cause cancer? Explain.

5. NAEP scores Young people have a better chance of full-time employment and good wages if they are good with numbers. How strong are the quantitative skills of young Americans of working age? One source
of data is the National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey, which is based on a nationwide probability sample of households. The NAEP survey includes a
short test of quantitative skills, covering mainly basic arithmetic and the ability to apply it to realistic problems. Scores on the test range from 0to 500. For example, a person who scores 233can add the amounts of two checks appearing on a bank deposit slip; someone scoring 325can determine the price of a meal from a menu; a person scoring 375 can
transform a price in cents per ounce into dollars per pound. Suppose that you give the NAEP test to an SRS of 840people from a large population in which the scores have mean 280and standard deviation蟽=60. The mean xof the 840 scores will vary if you take repeated samples.
(a) Describe the shape, center, and spread of the sampling distribution of x.
(b) Sketch the sampling distribution of x. Mark its mean and the values one, two, and three standard deviations on either side of the mean.
(c) According to the68鈥�95鈥�99.7rule, about 95%of all values of x炉lie within a distance mof the mean of the sampling distribution. What is m? Shade the region on the axis of your sketch that is within m of the mean.

(d) Whenever x炉falls in the region you shaded, the population mean 渭lies in the confidence intervalx卤m. For what percent of all possible samples does the interval capture 渭?

The Gallup Poll interviews 1600people. Of these, 18%say that they jog regularly. The news report adds: "The poll had a margin of error of plus or minus three percentage points at a 95%confidence level." You can safely conclude that

(a) 95%of all Gallup Poll samples like this one give answers within卤3%of the true population value.

(b) the percent of the population who jog is certain to be between 15%and21%.

(c) 95%of the population jog between5%and21%of the time.

(d) we can be 95%confident that the sample proportion is captured by the confidence interval.

(e) if Gallup took many samples,95%of them would find that 18%of the people in the sample jog.

18. Explaining confidence The admissions director from Big City University found that (107.8, 116.2) is a 95% confidence interval for the mean IQ score of all freshmen. Comment on whether or not each of the following explanations is correct.
(a) There is a 95%probability that the interval from 107.8to 116.2contains 渭.
(b) There is a 95%chance that the interval (107.8,116.2) contains x.
(c) This interval was constructed using a method that produces intervals that capture the true mean in 95% of all possible samples.
(d) 95%of all possible samples will contain the interval (107.8,116.2).

(e) The probability that the interval (107.8,116.2)captures 渭is either 0or 1, but we don鈥檛 know which.

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. which of the following would result in the smallest margin of error in estimating the mean salt content M?

(a) 90% confidence; n=25.

(b) 90% confidence; n=50.

(c) 95% confidence; n=25.

(d) 95%confidence; n=50.

(e) n=100 at any confidence level.
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