Find the margin of error for the survey. Then give an interval that is likely to contain the exact percent of all people in the county who ride a bike to work.

Question

In a survey of 865 people in a county, 61% said that they ride a bike to work. Find the margin of error for the survey. Then give an interval that is likely to contain the exact percent of all people in the county who ride a bike to work. Round each answer to the nearest tenth of a percent.

The margin of error is about ± ---%?

It is likely that the exact percent of all people in the county who ride a bike to work is between ---% and ---%?

Answer 1

The formula for margin of error is: MOE = z*(∂/√n) and for proportions, we know that ∂=p*(1-p)

I will use the z-value for a 95% confidence interval, which is 1.96.

So, we have MOE = 1.96*((0.61*0.39)/√865) = 0.016 = 0.02

Now, to compute a 95% confidence interval, we simply add and subtract the MOE from our estimate. We get (0.61 - 0.02, 0.61 + 0.02 ), or (0.59, 0.63).