Question

1. Explain what happens to the 95 % confidence interval as the sample size increases.
2. Explain what happens to the width of the confidence interval for a 99% interval versus a 95%.

Answer 1

1)

95% CI = Mean +/- ZCritical * Std Dev / n1/2

So, from the above equation, we can conclude that the Confidence Interval is inversely proportional to Sample Size.

Hence, as the sample size increases, 95% confidence interval decreases.

2)

Confidence Interval (CI) = Mean +/- ZCritical * Std Dev / n1/2

So, from the above equation, we can conclude that the Confidence Interval is directly proportional to Critical Value. ie as Critical Value increases, CI increases and vice versa.

Hence, the width of CI for 99% is larger (wider) than 95% as Critical Value for 99% is greater than 95%

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