Question

The mean percentage of a population of people eating out at least once a week is 57%, with a standard deviation of 3.5%. Assume that a sample size of 40 people was surveyed from the population an infinite number of times. In which interval will 95% of the sample means occur?

Answer 1

Taking samples of 40 people an infinite number of times results in the distribution of the sample means closely approaching a Normal distribution with the following parameters:
Mean = population mean
Standard deviation = population standard deviation/square root of the sample size.
The interval in which 95% of thesample means occur is as follows:
\[(57-1.96\times \frac{3.5}{\sqrt{40}}\ ,\ 57+1.96\times \frac{3.5}{\sqrt{40}})\]

Answer 2

im still confused, like where do i go from there?

Answer 3

@tcarroll010

Answer 4

@pascuzzoa Just calculate the two values inside the brackets.

Answer 5

@pascuzzoa on one side of the comma is an equation on the other is a seperate equation they will give you seperate values think of it as a minimum and a maximum this is the answer between 55.89% and 58.11%

Answer 6

@kropot72

Answer 7

@levils Basically, you are correct.