Question

A record book has 3 confidence intervals listed (2,3) (1,2), and (1.5, 3.) for the samwe parameter. The scientist was told one of them was record from a faulty instrument, the 2nd a 95% confidence interval and the 3rd a 99% confidence interval. But they don't know which is which. Which of the following is true?

O (1,2) is 99% CI, (2,3) is 95% CI, (1.5, 3.5) is the error
O (2,3) is 99% CI, (1.5,3.5) is 95% CI, (1,2) is the error
O (2,3) is 95% CI, (2,3) is 95% CI, (1,2) is the error
O (1,2) is 95% CI, (2,3) is 99% CI, (1.5, 3.5) is the error

Answer 1

Explanation:

Given are three confidence intervals as (2,3) (1,2), and (1.5, 3.)

If for same data these are confidence intervals, then mid value should be the same

(2,3) mid value = 2.5

(1,2) mid value = 1.5

(1.5,3.5) midvalue = 2.5

1.5 is very far from other two so (1,2) is wrong

Out of other two, 1.5,3.5 is wider. Hence i.e. 99%

So correct answer is

O (2,3) is 95% CI, (2,3) is 99% CI, (1,2) is the error