An article included data from a survey of 1,016 hiring managers and human resource professionals. The
article noted that many employers are using social networks to screen job applicants. Of the 1,016 people
who participated in the survey, 693 indicated that they use social networking sites 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, p̂. What is the value of p̂ for this sample? (Round your
answer to four decimal places.)
(b) Based on what you know about the sampling distribution of p̂, 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.
(Round your answer to four decimal places.)
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(a) The value of p̂, the sample proportion of hiring managers and human resource managers who use social networking sites to research job applicants, is calculated by dividing the number of people who indicated they use social networking sites (693) by the total number of participants in the survey (1,016).
p̂ = 693/1,016
p̂ ≈ 0.6827
Therefore, the value of p̂ for this sample is approximately 0.6827.
(b) The sampling distribution of p̂ can be approximated by a normal distribution when the sample size is large enough, based on the Central Limit Theorem. With a sample size of 1,016, which is relatively large, it is reasonable to assume that the sampling distribution of p̂ is approximately normal.
To determine if it is reasonable to think that this estimate is within 0.02 of the actual value of the population proportion, we need to consider the standard error of p̂. The standard error, denoted as σp̂, can be calculated using the formula:
σp̂ = √(p̂(1-p̂)/n)
where p̂ is the sample proportion and n is the sample size.
In this case, we can use the sample proportion p̂ of approximately 0.6827.
σp̂ = √(0.6827(1-0.6827)/1,016)
σp̂ ≈ 0.0129
The standard error of p̂ is approximately 0.0129.
Considering a margin of error of 0.02, the estimate of p, the population proportion, is reasonably within 0.02 of the actual value if:
0.02 ≤ 2 * σp̂
0.02 ≤ 2 * 0.0129
0.02 ≤ 0.0258
Since 0.02 is less than or equal to 0.0258, it is reasonable to think that this estimate is within 0.02 of the actual value of the population proportion.
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