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Math-John, PhD in Statistics

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Consider the formula used for any confidence interval and the

Resolved Question:

Consider the formula used for any confidence interval and the elements included in that formula. What happens to the confidence interval if you (a) increase the confidence level, (b) increase the sample size, or (c) increase the original sample statistic? Only consider one of these changes at a time. Explain your answer with words and by referencing the formula.

Hi, I am working on it and will post the answer shortly.

johnczheng :

The formula for confidence interval is: (Sample statistic - (standard error) * (critical value), Sample statistic + (standard error) * (critical value)) (a) as confidence level increases, the critical value also increases, so confidence interval will become wider. (b) as sample size increases, the standard error will become smaller, so confidence interval will become narrower. (c) sample statistic is the center of the confidence interval. So as this increases, the confidence interval shift to the right but the width stays same.

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