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).
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: 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%.
