Two Tailed Test

A two-tailed test occurs when the null hypothesis is of the type:

H₁: μ≠ μ₀

H₁: p≠ p₀

The alternative hypothesis, therefore, is of the type:

H₁: μ≠ μ₀

H₁: p≠ p₀

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:

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: 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, H₀, should be accepted with a confidence level of 95%.