Question

How do you determine significance based on confidence intervals?

1. If using a ONE SAMPLE t-test, and the null hypothesis is H0: u = 100, if the confidence interval interval contains 100 (for instance, the interval is [70, 136]), is the result NOT significant?

2. If using an TWO INDEPENDENT groups t-test, and the null hypothesis is H0: u1 = u2, if the confidence interval contains 0 (for instance, the interval is [-1, 5]), is the result NOT significant?

Basically, I need to know the difference between which value is important to determine significance using confidence intervals for both kinds of t-tests.

Answer 1

## How do you determine significance based on confidence intervals?

if interval include null value then result is not significant . and if interval free from null value then result is significant .

1. If using a ONE SAMPLE t-test, and the null hypothesis is H0: u = 100, if the confidence interval interval contains 100 (for instance, the interval is [70, 136]), is the result NOT significant?

Answer : Interval is free from null value and u = 100 is include the interval hence the result is significant . at given level .

and we reject Ho .

2. If using an TWO INDEPENDENT groups t-test, and the null hypothesis is H0: u1 = u2, if the confidence interval contains 0 (for instance, the interval is [-1, 5]), is the result NOT significant?

Answer : we have given confidence interval for the difference between means .

interval is -1 to 5 interval include null value hence result is not significant .

here we fail to reject Ho that is population means are equal .

## note : In testing there are p value approach , critical value approach and confidence interval .

we can use above approach and can conclusion .