The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion ?
Question
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion ?
Solution
To calculate the standard error of the proportion, we first need to find the sample proportion (p̂) and then use the formula for the standard error of a proportion.
Step 1: Calculate the sample proportion (p̂) The sample proportion is calculated as the number of successes (in this case, employees using Facebook during work hours) divided by the sample size.
p̂ = 53 / 150 = 0.3533
Step 2: Calculate the standard error of the proportion The formula for the standard error of a proportion is:
SE = sqrt [ p̂(1 - p̂) / n ]
where:
- p̂ is the sample proportion
- n is the sample size
Substituting the values we have:
SE = sqrt [ 0.3533(1 - 0.3533) / 150 ] SE = sqrt [ 0.3533 * 0.6467 / 150 ] SE = sqrt [ 0.2284 / 150 ] SE = sqrt [ 0.00152 ] SE = 0.039
So, the standard error of the proportion is approximately 0.039.
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