Suppose you compute a confidence interval with a sample size of 80. What will happen to the confidence interval if the sample size decreases to 22?The confidence interval will widen.The confidence interval will narrow.The width of the confidence interval will stay the same.
Question
Suppose you compute a confidence interval with a sample size of 80. What will happen to the confidence interval if the sample size decreases to 22?The confidence interval will widen.The confidence interval will narrow.The width of the confidence interval will stay the same.
Solution
To answer this question, let's break it down step by step:
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Understanding Confidence Interval: A confidence interval provides a range of values that is likely to contain the population parameter. It is influenced by the sample size, the variability in the data, and the confidence level.
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Effect of Sample Size: The width of the confidence interval is inversely related to the sample size. This means that as the sample size increases, the confidence interval becomes narrower, and as the sample size decreases, the confidence interval becomes wider.
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Given Scenario: Initially, the sample size is 80. If the sample size decreases to 22, we need to determine the effect on the confidence interval.
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Conclusion: Since the sample size is decreasing from 80 to 22, the confidence interval will widen.
Therefore, the correct answer is: The confidence interval will widen.
Similar Questions
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