Question

Suppose a department store wants to estimate u, the average age of the customers in its contemporary apparel department, within 2 years with 95% confidence. Approximately how large a sample would be required? The standard deviation is 7.5 years.

Answer 1

To estimate the average age of customers in the contemporary apparel department of a department store within 2 years and with 95% confidence, you would need a sample size of approximately 170 customers.

Step-by-step explanation:

To estimate the average age of customers in the contemporary apparel department of a department store within 2 years and with 95% confidence, we can use the formula for the sample size. The formula is given by:

• n = (Z * sigma / E)^2

where n is the sample size, Z is the z-score corresponding to the confidence level (in this case, 95% confidence is equivalent to a z-score of 1.96), sigma is the standard deviation, and E is the maximum error margin (in this case, 2 years).

Plugging in the values, we get:

• n = (1.96 * 7.5 / 2)^2
• n ≈ 169.65

So, we would need a sample size of approximately 170 customers to estimate the average age within 2 years with 95% confidence.