# Two Tailed Test

A two-tailed test occurs when the null hypothesis is of the type **H _{0}: μ = k** (or

**H**) and the alternative hypothesis, therefore, is of the type

_{0}: p = k**H**(or

_{1}: μ≠ k**H**).

_{1}: p≠ k 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:

or:

#### 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:

**H _{0} : μ = 6 ** The average test score has not varied.

**H _{1} : 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: z_{α/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, H_{0}, should be accepted with a confidence level of 95%.