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Chapter 11: Q.11.2 (page 459)

Why is statistical inference generally used to obtain information about a population proportion?

Short Answer

Expert verified

It is quite difficult to obtain information on a population proportion by examining all of the population's individuals so we sample the population by taking a group of people that are representative of the entire population.

Step by step solution

01

Given information

We need to find that to obtain information about a population proportion why generally use statistical inference

02

Explanation

It is quite difficult to obtain information on a population proportion by examining all of the population's individuals. Taking a census of a big population is often impractical or impossible.

As a result, sampling is carried out. We sample the population by taking a group of people that are representative of the entire population.

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Most popular questions from this chapter

Suppose that you can make reasonably good educated guesses, p^1gand p^2g, for the observed values of p^1and p^2.

a. Use your result from Exercise 11.132to show that a (1-伪)-level confidence interval for the difference between two population proportions that has an approximate margin of error of Ecan be obtained by choosing

n1=n2=p^1g1-p^1g+p^2g1-p^2gza/2E2

rounded up to the nearest whole number. Note: If you know likely ranges instead of exact educated guesses for the observed values of the two sample proportions, use the values in the ranges closest to 0.5as the educated guesses.

b. Explain why the formula in part (a) yields smaller (or at worst the same) sample sizes than the formula in Exercise 11.133.

c. When reasonably good educated guesses for the observed values of p^1and p^2can be made, explain why choosing the sample sizes by using the formula in part (a) is preferable to choosing them by using the formula in Exercise 11.133.

In discussing the sample size required for obtaining a confidence interval with a prescribed confidence level and margin of error, we made the following statement: "If we have in mind a likely range for the observed value of p^, then, in light of Fig. 11.1, we should take as our educated guess for p^the value in the range closest to 0.5"Explain why.

Indicted Governor. On Thursday, June 13, 1996, thenArizona Governor Fife Symington was indicted on 23counts of fraud and extortion. Just hours after the federal prosecutors announced the indictment, several polls were conducted of Arizonans asking whether they thought Symington should resign. A poll conducted by Research 91影视, Inc., that appeared in the Phoenix Gazette, revealed that 58%of Arizonans felt that Symington should resign; it had a margin of error of plus or minus 4.9 percentage points. Another poll, conducted by Phoenix-based Behavior Research Center and appearing in the Tempe Daily News, reported that 54% of Arizonans felt that Symington should resign; it had a margin of error of plus or minus 4.4 percentage points. Can the conclusions of both polls be correct? Explain your answer.

Body Mass Index. Body mass index (BMI) is a measure of body fit based on height and weight. According to the document Dietary Guidelines for Americans, published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI of greater than 25 indicates an above healthy weight (i.e., overweight or obese), Oct 750 randomly selected adults whose highest degree is a bachelor's, 386 have an above healthy weight; and of 500 randomly selected adults with a graduate degree, 237 have an above healthy weight.

a. What assumptions are required for using the two-proportions z-lest here?

b. Apply the two-proportions z-test to determine, at the 5% significance level, whether the percentage of adults who have an above healthy weight is greater for those whose highest degree is a bachelor's than for those with a graduate degree.

a. Determine the sample proportion.

b. Decide whether using the one-proportion z-test is appropriate.

c. If appropriate, use the one-proportion z-test to perform the specified hypothesis test.

x=16

n=20

H0:p=0.7

Ha:p鈮�0.7

a=0.05
See all solutions

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