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.

Question

Camron Carey

Mathematics

1 September, 09:12

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.

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Cristofer Kirby · 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).