Question

The article "Career Expert Provides DOs and DON'Ts for Job Seekers on Social Networking" (CareerBuilder.com, August 19,2009 ) included data from a survey of 2,667 hiring managers and human resource professionals. The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common. Of the 2,667 people who participated in the survey, 1,200 indicated that they use social networking sites (such as Facebook, MySpace, and LinkedIn) to research job applicants. For the purposes of this exercise, assume that the sample can be regarded as a random sample of hiring managers and human resource professionals. a. Suppose you are interested in learning about the value of \(p,\) the proportion of all hiring managers and human resource managers who use social networking sites to research job applicants. This proportion can be estimated using the sample proportion, \(p .\) What is the value of \(p\) for this sample? b. Based on what you know about the sampling distribution of \(p,\) is it reasonable to think that this estimate is within 0.02 of the actual value of the population proportion? Explain why or why not.

Short answer

a) Approximately 0.45 or 45%. b) Assuming the Central Limit Theorem, and given that the sample size is large enough, it is reasonable to think that this estimate could be within 0.02 of the actual population proportion.

Step-by-step solution

Calculate the Sample Proportion

You can calculate sample proportion (denoted as \( p \)) by dividing the number of successes (in this case, the number of hiring managers and human resource professionals that use social networking sites for applicant research, which is 1,200) by the total number of trials (which in this case is the number of all participating professionals, which is 2,667). So, the formula would be: \( p = \frac{1200}{2667} \).

Calculate the Result

By doing the calculation from Step 1, the value of the sample proportion, \( p \), comes out to be approximately 0.45. This interpretation of this value signifies that about 45% of hiring managers and human resource professionals use social networking sites for applicant research.

Making Inferences about the Population Proportion

Knowing that the sample is a random sample from the population of interest, by the Central Limit Theorem, we can assume the sampling distribution of \( p \) will be approximately normal if the sample size is large enough (usually if np and n(1-p) are both greater than 5). Here \( np = 0.45*2667 = 1200.15\) and \( n(1-p) = 1466.85 \), which are both greater than 5. Hence, it's reasonable to think that the estimate could be within 0.02 of the actual population proportion.