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, 90% said that the appearance of a job applicant is most important for a good first impression.


a. Among the 514 human resource professionals who were surveyed, how many of them said that the appearance of a job applicant is most important for a good first impression?

Verified step by step guidance

1. Step 1: Identify the given information. The total number of human resource professionals surveyed is 514, and the proportion (p̂) of those who said appearance is most important is 90%, or 0.90.
2. Step 2: To find the number of professionals who said appearance is most important, use the formula: \( \text{Number} = p̂ \times \text{Total Surveyed} \).
3. Step 3: Substitute the given values into the formula: \( \text{Number} = 0.90 \times 514 \).
4. Step 4: Perform the multiplication to calculate the number of professionals. This will give you the total count of those who prioritized appearance.
5. Step 5: Verify the result to ensure it is a whole number, as the number of people cannot be fractional. If necessary, round to the nearest whole number.

Key Concepts

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. For example, if a 95% confidence interval for a population proportion is calculated, it means that if we were to take many samples and build intervals in this way, approximately 95% of those intervals would contain the true proportion.

Sample Proportion

The sample proportion is the ratio of the number of successes in a sample to the total number of observations in that sample. In the context of the question, it refers to the percentage of surveyed human resource professionals who believe that appearance is crucial for a good first impression, which is 90% in this case.

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 prioritize appearance. In this scenario, while the sample provides an estimate, the actual population parameter remains unknown and is what the confidence interval aims to estimate.