Quiz: QZ-20261001-91265

Quiz Details

QZ-20261001-91265

Topics:

Sample size derminantion for experimental designs

Difficulty: Level 5 - Very Hard

Questions: 15

Language: English (English)

Generated: October 01, 2026 at 03:26 PM

Generated by: Patience Juliet

Instructions: Select an answer for each question and click "Check Answer" to see if you're correct. Then view the explanation to learn more!

1 What is the primary factor influencing sample size in determining the power of a statistical test?

A) Sample variability

B) Population size

C) Effect size

D) Significance level

Correct Answer: C
Explanation: Effect size is the magnitude of the difference or relationship being tested. A larger effect size generally requires a smaller sample size to achieve the same power.

2 In a two-sample t-test, what is the relationship between sample size and the confidence interval for the difference in means?

A) Confidence intervals are only affected by the standard deviation.

B) Larger sample sizes lead to wider confidence intervals.

C) Sample size has no effect on confidence intervals.

D) Larger sample sizes lead to narrower confidence intervals.

Correct Answer: D
Explanation: As sample size increases, the standard error decreases, which results in narrower confidence intervals for the difference in means.

3 Which of the following is typically NOT a consideration when determining sample size for an experimental design?

A) The color of the experimental materials

B) The number of treatment groups

C) The method of data analysis

D) The desired significance level

Correct Answer: A
Explanation: While the significance level, number of groups, and analysis method are crucial for sample size determination, the color of materials is irrelevant.

4 What is the purpose of conducting a power analysis in the context of sample size determination?

A) To identify the minimum sample size needed to detect an effect.

B) To determine the exact population size required for the study.

C) To define the statistical method to be used.

D) To maximize the sample size regardless of costs.

Correct Answer: A
Explanation: Power analysis helps researchers identify the minimum sample size needed to detect a specified effect size with a given level of power.

5 Which of the following sample size determination methods is based on the assumption of a normal distribution?

A) Central Limit Theorem

B) Cohen's d

C) Binomial Distribution

D) Fisher's Exact Test

Correct Answer: A
Explanation: The Central Limit Theorem states that the sampling distribution of the sample mean will approximate a normal distribution, which underpins many sample size determination methods.

6 When is it appropriate to use a sample size formula that incorporates the finite population correction?

A) When the sample size is small relative to the population size.

B) When the population is infinite.

C) When the population size is small relative to the sample size.

D) When the effect size is large.

Correct Answer: C
Explanation: The finite population correction is used when the sample size approaches a significant fraction of the total population, as it adjusts for the reduced variability.

7 In experimental designs, what does the term 'margin of error' refer to?

A) The error associated with random sampling.

B) The maximum difference allowed between the population parameter and the sample statistic.

C) The likelihood of making a Type I error.

D) The confidence level of the study.

Correct Answer: B
Explanation: Margin of error indicates the range within which the true population parameter is expected to lie, based on the sample statistic.

8 What factor is NOT directly related to the sample size when aiming for a high level of statistical power?

A) Variability of the data

B) Significance level

C) Effect size

D) Sample collection method

Correct Answer: D
Explanation: While the sample collection method may affect the quality of data, it does not directly determine the sample size needed to achieve a particular statistical power.

9 What is the implication of a larger sample size in terms of statistical significance?

A) It has no impact on Type I error rates.

B) It increases the likelihood of finding a statistically significant result.

C) It ensures that the results are practically significant.

D) It decreases the level of Type II errors only.

Correct Answer: B
Explanation: With larger sample sizes, the standard error decreases, making it easier to detect statistically significant effects even if they are small.

10 What is the general rule of thumb regarding sample size for experiments involving multiple groups?

A) Larger sample sizes should only be used for the control group.

B) Sample sizes can be unequal if the effect size is known.

C) Use the same sample size for each group.

D) Sample size has no relation to the number of groups.

Correct Answer: C
Explanation: Using equal sample sizes across treatment groups is often recommended, as it simplifies analysis and increases statistical power.

11 Which of the following is LEAST likely to affect the required sample size for a clinical trial?

A) Expected effect size

B) Anticipated dropout rate

C) Duration of the trial

D) Standard deviation of the outcome measure

Correct Answer: C
Explanation: While the duration of the trial is important for other reasons, it does not directly affect the sample size calculation for achieving power.

12 In a power analysis, if the significance level is set to 0.01 instead of 0.05, what is the expected impact on sample size?

A) Sample size will increase.

B) Sample size is not influenced by significance level.

C) Sample size will remain the same.

D) Sample size will decrease.

Correct Answer: A
Explanation: A lower significance level (0.01) increases the required sample size to maintain the same power, as it becomes harder to detect an effect.

13 What is the primary reason for using a larger sample size in longitudinal studies?

A) To simplify data analysis.

B) To increase generalizability.

C) To minimize the effects of attrition.

D) To reduce costs.

Correct Answer: C
Explanation: Larger sample sizes help compensate for potential attrition over time, ensuring that the study retains sufficient power as participants drop out.

14 When considering ethical implications, what is a key factor in determining sample size for human studies?

A) The availability of participants.

B) Minimizing participant exposure to risk.

C) The length of the study.

D) The cost of materials.

Correct Answer: B
Explanation: Ethically, researchers aim to use the smallest sample size necessary to achieve reliable results while minimizing participant risk.

15 What statistical measure is often used to estimate the necessary sample size when dealing with proportions?

A) Standard deviation

B) Z-score

C) Chi-square

D) Cohen's d

Correct Answer: B
Explanation: The Z-score is commonly used when calculating sample sizes for proportions, as it relates to the normal distribution of sample means.

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