Chapter 20 estimating proportions with confidence


Answer: the true margin of error found by the formula 2



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Answer: the true margin of error found by the formula 2 (S.d.) is always less than or equal to this value. it is equal when the proportion used in the formula for S.D. is .50.


  1. The formula for calculating a confidence interval for a population proportion is based on the rule of sample proportions, which has assumptions that need to be met. What is the most important assumption that you need to check before applying the confidence interval formula to a sample proportion?

Answer: the sample size must be large enough so that you are likely to see at least five of each of the two possible responses or outcomes.



  1. Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population.

    1. In 95% of all samples, the sample proportion will fall within 2 standard deviations of the mean, which is the true proportion for the population.

    2. In 95% of all samples, the true proportion will fall within 2 standard deviations of the sample proportion.

    3. If we add and subtract 2 standard deviations to/from the sample proportion, in 95% of all cases we will have captured the true population proportion.

    4. All of the above.

Answer: d


  1. Sampling methods and confidence intervals are routinely used for financial audits of large companies. Which of the following is an advantage of doing it this way, versus having a complete audit of all records?

    1. It is much cheaper.

    2. A sample can be done more carefully than a complete audit.

    3. A well-designed sampling audit may yield a more accurate estimate than a less carefully carried out complete audit or census.

    4. All of the above.

Answer: d


  1. In which of the following situations can you construct a confidence interval for the population proportion with only what is given?

    1. The sample proportion and the margin of error.

    2. The sample proportion and the sample size.

    3. The number of individuals in the sample with the trait of interest, and the total sample size.

    4. All of the above.

Answer: d


  1. In which of the following situations can a confidence interval provide useful information for making a decision?

    1. To assess whether or not at least 90% of a company’s financial entries are correct.

    2. To estimate the percentage of married couples in which the wife is taller than the husband.

    3. To help determine whether or not someone has ESP (versus just being a lucky guesser).

    4. All of the above.

Answer: d


  1. To obtain a 99.7% (virtually all-encompassing) confidence interval for the true population proportion, you would add and subtract about __________ standard deviations to/from the sample proportion.

Answer: three


  1. Using the same sample data, the margin of error for an 80% confidence interval is __________ than the margin of error for a 90% confidence interval.

Answer: larger

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