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Suppose you compute a confidence interval with a sample size of 46. What will happen to the confidence interval if the sample size decreases to 30?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 46. What will happen to the confidence interval if the sample size decreases to 30?The confidence interval will widen.The confidence interval will narrow.The width of the confidence interval will stay the same.

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Solution

The confidence interval will widen. This is because the confidence interval is inversely proportional to the square root of the sample size. So, when the sample size decreases, the confidence interval increases or widens. This is due to the fact that with a smaller sample size, there is more uncertainty, hence a wider confidence interval.

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