our place of employment is trying to determine whether to allow its employees to work from home for 2 days a week. Knowing that you’ve previously taken a statistics course, your boss asks you to “figure it out”. You create a survey to gauge employee interest in this area. 1. Formerly, your place of employment has tried to give surveys to everyone, a census, but only a few people responded to the email. Your new plan is to randomly choose some employees and administer the survey yourself. You put everyone’s name on a numbered list and randomly choose numbers until you have your sample. What form of sampling is being described here?
Your place of employment is trying to determine whether to allow its employees to work from home for
2 days a week. Knowing that you’ve previously taken a statistics course, your boss asks you to “figure it
out”. You create a survey to gauge employee interest in this area.
1. Formerly, your place of employment has tried to give surveys to everyone, a census, but only a few
people responded to the email. Your new plan is to randomly choose some employees and administer
the survey yourself. You put everyone’s name on a numbered list and randomly choose numbers until
you have your sample. What form of sampling is being described here?
2. Suppose you want to estimate the percentage of employees who want to work from home. Doing
some research on the internet, you find a recent study that found that 72% of employees prefer a hybrid
remote-office model. Using that value as your sample proportion, ?̂, estimate how many people you
would need to survey in order to estimate the percentage in your company that would prefer to work at
home, within 5 percentage points, with 95% confidence.
3. Because of practical considerations you ultimately decide to survey 100 people and find that 75 of
them would prefer to work at home to some extent. When your boss asks you “What percentage of
employees at this company want to work from home?”, what percentage do you tell him?
4. He seems flustered and asks “That’s higher than I thought! Since you didn’t ask everyone in the
company, how do you know that your numbers are correct?” What do you say in response?
5. Still unconvinced, you calculate a 95% confidence
who want to work from home. Show the calculation below or indicate what technology you used and
what values you put into the calculator or Excel.
6. Explain what this confidence interval means to your boss, who has never taken a statistics class.
7. Explain why the confidence interval is a better than just using the point estimate that you gave him
from question #3.
8. Your job is planning on expanding its benefits package to include some amount of student loan
forgiveness. Your survey also asked if the employees had student loans and how much they currently
owed. Your survey found that out of the 100 people surveyed, the mean amount of student loan debt
was $32,425, with a standard deviation of $16,824. Estimate the mean student loan debt for all
employees in your company, with 95% confidence using your sample data. Use the t-distribution here.
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