Two Tailed Test

A two-tailed test occurs when the null hypothesis is of the type H0: μ = k (or H0: p = k) and the alternative hypothesis, therefore, is of the type H1: μ≠ k (or H1: p≠ k).


Two Tailed Test


The significance level, α, is concentrated in two parts (or tails) symmetrical about the mean.

The limit of acceptance in this case is the corresponding confidence interval for μ or p, that is to say:

Confidence Interval

or:

Confidence Interval

Example

It is known that the standard deviation of the scores in a math exam was 2.4 and a sample of 36 students scored an average of 5.6. With this data, can the hypothesis be confirmed that the average test score was 6 with a confidence level of 95%?

1. State the null and alternative hypotheses:

H0 : μ = 6      The average test score has not varied.

H1 : μ ≠ 6       The average test score has varied.

2. Calculate the limit of acceptance:

For a significance level of α = 0.05, the corresponding critcal value is: zα/2 = 1.96.

Calculate the confidence interval for the mean:

(6 − 1.96 · 0.4, 6 + 1.96 · 0.4) = (5.22, 6.78)

3. Verify:

The value of the mean of the sample is: 5,6 .

4. Decide:

The nule hypothesis, H0, should be accepted with a confidence level of 95%.