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Question 1:

What is the relationship between sample size and statistical power?

A) Sample size has no effect on statistical power.
B) Larger sample size increases statistical power.
C) Smaller sample size increases statistical power.
D) Sample size and statistical power are unrelated.

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Explanation: The correct answer is B) Larger sample size increases statistical power. Statistical power is the probability of correctly rejecting a false null hypothesis. A larger sample size allows for a more accurate representation of the population, reduces sampling error, and increases the chances of detecting a true effect if it exists. Therefore, larger sample sizes generally lead to higher statistical power.

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Question 2:

What is the relationship between sample size and margin of error?

A) Sample size has no effect on the margin of error.
B) Larger sample size decreases the margin of error.
C) Smaller sample size decreases the margin of error.
D) Sample size and margin of error are unrelated.

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Explanation: The correct answer is B) Larger sample size decreases the margin of error. The margin of error is the measure of uncertainty in estimating a population parameter from a sample. With a larger sample size, there is a higher level of confidence that the sample mean or proportion is representative of the population. This increased representativeness reduces the variability and, consequently, the margin of error.

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Question 3:

Which of the following is true about sample size in experimental design?

A) Larger sample size is always better.
B) Smaller sample size is always better.
C) Sample size should be determined based on the research question.
D) Sample size has no impact on experimental design.

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Explanation: The correct answer is C) Sample size should be determined based on the research question. The appropriate sample size depends on several factors, including the research question, the desired level of precision, the expected effect size, and the available resources. It is crucial to determine an adequate sample size to ensure that the study has sufficient statistical power to detect meaningful effects and draw reliable conclusions.

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Question 4:

What is statistical power?

A) The probability of making a Type I error.
B) The probability of making a Type II error.
C) The probability of correctly rejecting a false null hypothesis.
D) The probability of correctly accepting a true null hypothesis.

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Explanation: The correct answer is C) The probability of correctly rejecting a false null hypothesis. Statistical power is the probability of correctly detecting a true effect or correctly rejecting a false null hypothesis. It is the ability of a statistical test to detect a significant difference or relationship when one exists. Higher statistical power indicates a greater ability to detect effects and make accurate conclusions.

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Question 5:

What is the purpose of a power analysis in experimental design?

A) To determine the appropriate sample size for a study.
B) To calculate the margin of error in the study.
C) To randomly assign participants to groups.
D) To analyze the data collected in the study.

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Explanation: The correct answer is A) To determine the appropriate sample size for a study. A power analysis is a statistical calculation used to determine the sample size needed to achieve adequate statistical power for the study. It takes into account factors such as the desired level of power, expected effect size, significance level, and variability. Conducting a power analysis helps researchers ensure that their study has a sufficient sample size to detect meaningful effects and draw reliable conclusions.