Question

Suppose a researcher is interested in understanding the variation in the price of store brand milk. a random sample of 36 grocery stores is selected from a population and the mean price of store brand milk is calculated. the sample mean is $3.13 with a standard deviation of $0.23. construct a 99% confidence interval to estimate the population mean.

Answer 1

The confidence interval extremities are given by the formula:
m +/- (z · σ / √n)

In your problem:
m = 3.13
σ = 0.23
n = 36
The z-score for a 99% confidence interval is 2.576

Therefore:
m - (z · σ / √n) = 3.13 - (2.576 · 0.23 / √36) = 3.031
m + (z · σ / √n) = 3.13 + (2.576 · 0.23 / √36) = 3.229

Therefore, the confidence interval is (3.031, 3.229).