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. 95% of the sample mean occurs between % and %. nextreset

Answer 1

Percentage, p = 57% = 0.57
Sample size, N = 40
Standard deviation, SD = 3.5% = 0.035
Confidence = 95%
At 95%, Z = 1.96

Range of true mean, x_bar = p +/- Z*Sqrt [p(1-p)/N] = 0.57+/- 1.96*Sqrt[0.57(1-0.57)/40] = 0.57+/- 0.153

Therefore,
x_bar ranges between 0.417 and 0.723 or 41.7% and 72.3%