Question

question 10.
a research and development engineer is preparing a report for the board of directors on the battery life of a new cell phone they have produced. at a 95% confidence level,
he has found that the battery life is 3.2 ± 1.0 days. he wants to adjust his findings so the margin of error is as small as possible.
which of the following will produce the smallest margin of error?
a. ○ increase the confidence level to 99%.

b. ○ decrease the confidence level to 90%.

c. ○ take a new sample from the population using the exact same sample size.

d. ○ increase the confidence level to 100%. this will assure that there is no margin of error.

Explanation:

To determine which option produces the smallest margin of error, we analyze the relationship between confidence level and margin of error:

• Option A: Increasing the confidence level (e.g., to 99%) increases the critical value (e.g., z - score or t - score), which increases the margin of error.
• Option B: Decreasing the confidence level (to 90%) decreases the critical value, which decreases the margin of error.
• Option C: Taking a new sample with the same size does not systematically reduce the margin of error (sampling variability remains similar).
• Option D: A 100% confidence level is impossible in practice (it would require including the entire population, and the margin of error would not be zero).

Answer:

B. Decrease the confidence level to 90%.