QuestionWhich of the following would result in the widest confidence interval? A sample size of 100 with confidence A sample size of 100 with confidence. A sample size of 30 with confidence. A sample size of 30 with confidence.
Studdy Solution
STEP 1
1. Confidence intervals are wider with higher confidence levels.
2. Confidence intervals are narrower with larger sample sizes.
3. We are comparing confidence intervals for the same population parameter.
STEP 2
1. Understand the relationship between confidence level, sample size, and confidence interval width.
2. Compare the given scenarios based on these relationships.
STEP 3
Understand the relationship: - A higher confidence level (e.g., vs. ) results in a wider confidence interval because it requires more certainty. - A larger sample size (e.g., 100 vs. 30) results in a narrower confidence interval because it provides more information about the population.
STEP 4
Compare the scenarios:
- Sample size of 100 with confidence: narrower due to larger sample size and lower confidence level.
- Sample size of 100 with confidence: wider than the first due to higher confidence level, but still benefits from the larger sample size.
- Sample size of 30 with confidence: wider than both scenarios with sample size 100 due to smaller sample size.
- Sample size of 30 with confidence: the widest because it combines the smallest sample size with the highest confidence level.
The scenario that results in the widest confidence interval is:
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