Final answer:
The standard error of the mean is calculated as the population standard deviation divided by the square root of the sample size. For the given data with a population standard deviation of $0.52 and a sample size of 36 theaters, the standard error comes out to $0.0867, rounded to four decimal places.
Step-by-step explanation:
The student's question involves calculating the standard error of the mean, which is a measure of how much sample means would vary from the population mean if different samples were taken from the same population. The standard error of the mean is calculated by taking the population standard deviation (σ) and dividing it by the square root of the sample size (n). Since the student provided all the necessary values, you can calculate the standard error using the following formula:
Standard Error (σx) = σ / √n
Using the provided information:
- Population standard deviation (σ) = $0.52
- Sample size (n) = 36
The calculation would be:
σx = $0.52 / √36
σx = $0.52 / 6
σx = $0.0867
Therefore, the standard error of the mean is $0.0867, rounded to four decimal places as required.