Question

select the correct answer. a restaurant owner wants to determine the effectiveness of his servers. the owner conducted a survey by asking 30 customers about the servers effectiveness, on a day when the restaurant had 450 customers. the owner found that 65% of those surveyed were satisfied with the service offered. assuming a 95% confidence level, which statement holds true? a. as the sample size is too small, the margin of error is 0.203. b. as the sample size is too small, the margin of error cannot be trusted. c. as the sample size is appropriately large, the margin of error is 0.171. d. as the sample size is appropriately large, the margin of error is 0.203.

Explanation:

Step1: Recall margin - of - error and sample size relationship

The margin of error is inversely proportional to the square root of the sample size. A small sample size leads to a large margin of error, and a large sample size leads to a small margin of error.

Step2: Analyze the given sample size

The restaurant owner surveyed 30 customers out of 450. A sample size of 30 is relatively small for a population of 450. When the sample size is too small, the margin of error is large, and the results may not be reliable.

Step3: Evaluate each option

• Option A: A small sample size leads to a large margin of error, not a margin of error of 0.203 necessarily just because the sample is small.
• Option B: When the sample size is too small, the margin of error is large and the results (and thus the margin - of - error value) cannot be trusted. This is correct.
• Option C: A large sample size would lead to a small margin of error, not a margin of error of 0.171 when the sample size is appropriately large.
• Option D: A large sample size gives a small margin of error, not a margin of error of 0.203 when the sample size is appropriately large.

Answer:

B. As the sample size is too small, the margin of error cannot be trusted.