Use the given information to find the minimum sample size required to estimate an unknown population mean.

How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 99% confidence that the sample mean is within $200 of the population mean, and the population standard deviation is known to be $1,100.

A) 117

B) 82

C) 201

D) 165

Question

Mathematics

Matthews

Today, 00:35

Use the given information to find the minimum sample size required to estimate an unknown population mean.

How many weeks of data must be randomly sampled to estimate the mean weekly sales of a new line of athletic footwear? We want 99% confidence that the sample mean is within $200 of the population mean, and the population standard deviation is known to be $1,100.

A) 117

B) 82

C) 201

D) 165

+3

Answers (1)

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Glenn · Answer 1

C) 201

Step-by-step explanation:

Margin of error = critical value * standard error

ME = CV * SE

Assuming n > 30, we can approximate CV with a normal distribution. At P = 99%, CV = 2.576.

SE = σ / √n

SE = 1100 / √n

Therefore:

200 = 2.576 * 1100 / √n

n = 201