In: Statistics and Probability
A newspaper infographic titled "Social Media Jeopardizing Your Job?" summarized data from a survey of 1,845 recruiters and human resource professionals. The infographic indicated that 52% of the people surveyed had reconsidered a job candidate based on his or her social media profile. Assume that the sample is representative of the population of recruiters and human resource professionals in the United States.
(a)
Use the given information to estimate the proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile using a 95% confidence interval. (Use a table or technology. Round your answers to three decimal places.
( . , )
Give an interpreation of the interval context
We are 95% confident that the mean number of recruiters and human
resource professionals who have reconsidered a job candidate based
on his or her social media profile falls within this interval.
We are 95% confident that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
There is a 95% chance that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
We are 95% confident that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls directly in the middle of this interval.
There is a 95% chance that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls directly in the middle of this interval.Give an interpretation of the interval in context.
Give an interpretation of the confidence level of 95%.
Of all possible random samples, 95% would result in an interval that includes the actual value of the population proportion.
Of all possible random samples, 95% would result in an interval that lies below the actual value of the population proportion.
Of all possible random samples, 5% would result in an interval that lies above the actual value of the population proportion.
Of all possible random samples, 95% would result in an interval that is centered at the actual value of the population proportion.
Of all possible random samples, 5% would result in an interval that includes the actual value of the population proportion.
(b)
Would a 90% confidence interval be wider or narrower than the 95% confidence interval from part (a)?
wider
narrower
Solution :
Given that,
n = 1845
Point estimate = sample proportion = = 0.52
1 - = 1-0.52 = 0.48
a) At 95% confidence level
= 1-0.95% =1-0.95 =0.05
/2
=0.05/ 2= 0.025
Z/2
= Z0.025 = 1.960
Z/2 = 1.960
Margin of error = E = Z / 2 * (( * (1 - )) / n)
= 1.960 * ((0.52*(0.48) /1845 )
= 0.022
A 95% confidence interval for population proportion p is ,
- E < p < + E
0.52 - 0.022 < p < 0.52 +0.022
0.498 < p < 0.543
(0.498 ,0.543 )
We are 95% confident that the true proportion of recruiters and human resource professionals who have reconsidered a job candidate based on his or her social media profile falls within this interval.
Of all possible random samples, 95% would result in an interval that includes the actual value of the population proportion.
b) narrower