Question

First, a 90 percent confidence interval is constructed from a sample size of 100. Then, for the same identical data, a 92 percent confidence interval is constructed. The width of the 90 percent interval is wider than the 92 percent confidence interval. True or false?

Answer 1

Answer:

The statement is False.

Step-by-step explanation:

The width of a (1 - α)% confidence interval for a  population parameter is:

$W=2\times CV\times SE$

Here,

CV = critical value

SE = standard error

The critical value is computed using the confidence level.

If the confidence level increases then the critical value also increases. And if the confidence level decreases then the critical value also decreases.

And as the critical value if directly proportional to the width of the interval, any change in the critical value has a direct effect on the width, i.e. as the critical value increases the width of the interval increases and vice-versa.

The confidence level 90% is less than the confidence level 92%.

So, the width of the 90% confidence interval will be narrower than the width of the 92% confidence interval.

Thus, the statement is False.