Question

Suppose it is desired to estimate the average time a customer spends in a particular store to within 5 minutes (e.g., + 5 minutes) at 99% reliability. It is estimated that the standard deviation of the times is 15 minutes. How large a sample should be taken to get the desired interval?

a. n = 60
b. n = 35
c. n = 299
d. n = 25

Answer 1

To estimate the average time a customer spends in a store within an interval of 5 minutes at 99% reliability, the sample size should be approximately 299.

Step-by-step explanation:

To estimate the average time a customer spends in a store within an interval of 5 minutes at 99% reliability, we need to determine the sample size (n). The formula to calculate the sample size is:

n = (Z * σ / E)^2

Where:

• n is the sample size
• Z is the Z-score corresponding to the desired level of confidence (99% which corresponds to a Z-score of approximately 2.576)
• σ is the standard deviation of the times (15 minutes)
• E is the desired margin of error (5 minutes)

Plugging in the values, we have:

n = (2.576 * 15 / 5)^2

n ≈ 299

Therefore, the correct answer is c. n = 299.

Answer 2

To estimate the average customer time in a store at 99% reliability with a 5-minute margin of error and a 15-minute standard deviation, the sample size formula is used. The calculation yields approximately 59.78, which is rounded up to 60 participants (Option A).

Step-by-step explanation:

To estimate the average time a customer spends in a store to within 5 minutes at 99% reliability with an estimated standard deviation of 15 minutes, we need to calculate the required sample size. We use the formula for the sample size of a confidence interval:

n = (Z*σ/E)^2

where n is the sample size, Z is the Z-score corresponding to the confidence level (99% in this case), σ is the standard deviation, and E is the margin of error.

For a 99% confidence level, the Z-score is approximately 2.576. Plugging in the values we get:

n = (2.576*15/5)^2

n = (2.576*3)^2

n = (7.728)^2

n = 59.78

Since we always round up in sample size calculations to ensure we have enough subjects, we would need at least 60 participants.

The correct answer is a. n = 60.