Critical Thinking. In Exercises 17–28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.

Job Interviews In a Harris poll of 514 human resource professionals, 45.9% said that body piercings and tattoos were big personal grooming red flags.

a. Among the 514 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big personal grooming red flags?

검증된 단계별 안내

Step 1: Understand the problem. We are tasked with finding the number of human resource professionals who said that body piercings and tattoos were big personal grooming red flags. This is a simple application of percentages, where we are given the total number of surveyed professionals (514) and the percentage (45.9%).

Step 2: Recall the formula for finding a percentage of a total. The formula is: \( \text{Number} = \text{Total} \times \left( \frac{\text{Percentage}}{100} \right) \).

Step 3: Substitute the given values into the formula. Here, \( \text{Total} = 514 \) and \( \text{Percentage} = 45.9 \). The formula becomes: \( \text{Number} = 514 \times \left( \frac{45.9}{100} \right) \).

Step 4: Simplify the fraction \( \frac{45.9}{100} \) to convert the percentage into a decimal. This gives \( 0.459 \). The formula now becomes: \( \text{Number} = 514 \times 0.459 \).

Step 5: Multiply the total number of surveyed professionals (514) by the decimal value (0.459) to find the number of professionals who said body piercings and tattoos were big personal grooming red flags. This will give the final result.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Confidence Interval

A confidence interval is a range of values, derived from sample statistics, that is likely to contain the true population parameter with a specified level of confidence. It provides an estimate of uncertainty around a sample statistic, such as a proportion. For example, if 45.9% of surveyed professionals indicated a preference, the confidence interval would help determine the range within which the true proportion of all professionals likely falls.

Sample Proportion

The sample proportion is the ratio of the number of successes (in this case, professionals who view body piercings and tattoos as red flags) to the total number of observations in the sample. It is calculated by dividing the number of affirmative responses by the total sample size. This value is crucial for constructing the confidence interval and understanding the survey results.

Population Parameter

A population parameter is a numerical value that summarizes a characteristic of an entire population, such as the true proportion of all human resource professionals who consider body piercings and tattoos as grooming red flags. In statistical analysis, we often use sample data to estimate this parameter, acknowledging that our estimates may vary due to sampling error.