Question

You are reading the draft of a scientific paper that your co-worker has written. In the paper, he draws a sample from a population and computes the following two confidence intervals for : A 95% confidence interval of (90.21,100.37) A 99% confidence interval of (93.61.98.53) How do you know your co-worker made a mistake? He computed more than one confidence interval using the same sample data. Your co-worker did not round to 3 decimal places in his confidence interval upper and lower bounds The 99% confidence interval should be wider than the 95% confidence interval He is not a statistic, so it doesn't make any sense to compute confidence intervals for it. There is nothing wrong with his statements.

Answer 1

The correct option is (C).

Explanation:

The general form of a confidence interval is:

`CI=SS\pm CV\cdot SE`

Here,

SS = Sample statistic

CV = critical value

SE = standard error

The width of the confidence interval is:

`\text{Width}=2\cdot CV\cdot SE`

The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.

As the confidence level increases the critical value increases hence in turn increasing the width of the interval.

And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.

In this case the 95% confidence interval is, (90.21,100.37).

And the 99% confidence interval is, (93.61.98.53).

It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.

The correct option is (C).