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Chapter 9: Q 34. (page 567)

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within 3 percentage points of the results of this survey.

Short Answer

Expert verified

The results do not need to be in same margin of results. "At least" expression is wrong,

Step by step solution

01

Given Information

It is given that:

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20polls, the results of at least 19surveys would be within 3percentage points of the results of this survey.

02

Explanation

The results of 19among does not need to be in margin of results as it can give results which are not accurate for entire population.

It would have been correct to interpret that 19/20has confidence intervals that contain true population proportion.

Also it is possible that less than 19surveys have true population, it means "at least" is also incorrect.

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Most popular questions from this chapter

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

How much juice? Refer to Exercise 3. The mean amount of liquid in the bottles is 179.6ml and the standard deviation is 1.3ml. A significance test yields a P-value of 0.0589. Interpret the P-value.

Flu vaccine Refer to ExerciseR9.5. Of the 1000 adults who were given the vaccine, 43 got the flu. Do these data provide convincing evidence to support the company’s claim?

Ski jump When ski jumpers take off, the distance they fly varies considerably depending on their speed, skill, and wind conditions. Event organizers must position the landing area to allow for differences in the distances that the athletes fly. For a particular competition, the organizers estimate that the variation in distance flown by the athletes will be \(\sigma=10\) \(\sigma=10\) meters. An experienced jumper thinks that the organizers are underestimating the variation.
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