Calculate the margin of error for this survey. Round the percentage to one decimal place. Do not round intermediate steps

Question

fear of the dark is quite common among children. However, what about adults? One polling agency released the results of a survey that asked people over 40

 years old if they keep the lights on at night. Among 733

 respondents, 46%

 indeed leave the light on when going to sleep.

Calculate the margin of error for this survey. Round the percentage to one decimal place. Do not round intermediate steps.

If 46%

of 733

respondents keep the lights on at night, the margin of error is

Answer 1

Margin of Error for proportions is calculated by:

Z * √((p-hat)(1-p-hat)/n)

Z is the z-value corresponding to the confidence level desired. In this case, there is not a specific confidence level mentioned, so this would assume the default CL of 95% for the middle 95% of values in a normal distribution, the z value is +/- 1,96, so use 1.96 to calculate ME.

p-hat is the sample proportion (in this case, .46)

n is the sample size (in this example, 733)

so set up the problem and compute: 1.96 (√((.46*.54)/733)