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

95% C.I. = mean + or - 1.96(standard deviation / sqrt(sample size))
95% C.I. = 57 + or - 1.96(3.5/sqrt(40) = 57 + or - 1.085 = 57 - 1.085 to 57 + 1.085 = 55.92 to 58.09

Therefore, 95% of the mean will occur in the interval 55.92 to 58.09