If you had sampled 1000 dogs instead of 100 dogs, your confidence interval would have been smaller.

Question

BlackTom AI · Accepted Answer

Consider what happens to a confidence interval when sample size grows.
Option 1: 'Always True' — In most standard sampling scenarios, increasing the sample size from 100 to 1000 reduces the standard error and thus narrows the confidence interval, assuming the confidence level and estimator remain the same. This aligns with the general relationship that CI width is inversely related to the square root of n. However, there are edge cases (e.g., unusual sampling schemes or non-standard estimators) where the intuition might be nuanced, but for the common case of estimating a proportion or mean with a fixed confidence level, this statement is effectively true.
Option 2: 'Typically True' — This acknowledges that, in ordinary practice, larger samples yield smaller CIs, but it also hedges to reflect that there could be unusual situations (like non-random sampling or rule changes) where the CI behavior might not follow the standard pattern exactly. It’s the more cautious, commonly used phrasing in some textbooks when emphasizing general tendency rather than an absolute rule.
Option 3: 'Not Expected to be True' — This would be misleading. With more data, uncertainty typically decreases, not increases or remains the same, under standard conditions. Rejecting the usual relationship between sample size and CI width contradicts core statistical principles.
Option 4: 'False' — If interpreted as a blanket statement that increasing sample size never affects CI width, this would be incorrect under standard methodology. The standard theory indicates a smaller CI with larger n, so labeling this as false ignores the established relationship between n and precision.
Overall, the core idea is that larger samples generally produce more precise estimates, shrinking the confidence interval, with the caveat that exceptional design or estimator choices could alter the exact behavior in unusual cases.

CIS-124-HYA-CRN48380 Section 22 Practice

If you had sampled 1000 dogs instead of 100 dogs, your confidence interval would have been smaller.

View Explanation

Log in for full answers

Similar Questions

In a consumer society, many adults channel creativity into buying things

Economic stress and unpredictable times have resulted in a booming industry for self-help products

People born without creativity never can develop it

A product has a selling price of $20, a contribution margin ratio of 40% and fixed cost of $120,000. To make a profit of $30,000. The number of units that must be sold is: Type the number without $ and a comma. Eg: 20000

Which of the following statement regarding cost is correct:

Under the assumptions used in cost-volume-profit analysis, as the activity increases:

The CVP and break-even analysis are supported by a range of important assumptions. Which of the following is not an assumption of the CVP:

The break-even point is that at which:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler