Question

Confidence Intervals, explain the theory behind it. WHY is the 90% smaller??

Explain why the 90% confidence interval for the proportion of mothers who gave birth to a low birth weight child (part a above) is smaller than the 99% confidence interval given in part b.

Answer 1

The size of a confidence intervals depends on 3 things, one of which is the confidence level.

Higher the confidence level, the wider the interval is.

This is because confidence level refers to the percentage of all possible samples that can be expected to include the true population parameter.

For example, suppose all possible samples were selected from the same population, and a confidence interval computed for each sample. A 90% confidence level implies that 90% of the confidence intervals would include the true population parameter. 10% of the intervals won’t contain the parameter.

68% of data- 95% of data 99.7% of data -3 2 3 -2 -1 0 1 68% confidence interval 95% confidence interval 99% confidence interval

Now if you want that 99% of confidence interval should contain true population parameter and only 1% should not. So you need to wider band or large number of samples for this.

Mathematically,

x z Vn

Now CI depends upon Z-score from above formula

For 90% confidence interval, z-score will be less since area covered in above diagram of normal distribution wiill be less as compared to 99% Confidence interval.

Hence 99% has wider band as compared to 90%