What is the relationship between confidence intervals and hypothesis tests?

Confidence Interval:

Confidence interval is the interval estimate of the population parameter. It is the range where the population parameter value will lie in between.

The form of the confidence interval is,

CI = Point estimate ± Margin of error

The 100*(1–α)% confidence level means 100*(1–α)% of all possible sample values within the confidence interval will have the population parameter value and 100*α%  of sample values within the confidence interval will not have the population parameter.

Null and alternative hypotheses:

Null hypothesis:

Null hypothesis is a statement which is tested for statistical significance in the test. The decision criterion indicates whether the null hypothesis will be rejected or not in the favor of alternative hypothesis. In other words it can be said that, the null hypothesis is a statement which indicates the relationship between statistical measurements, distributions or categories. More often, null hypothesis states no significance relationship between variables or populations. But, null does not indicate “0” all the time.

Alternative hypothesis:

Alternative hypothesis is contradictory statement of the null hypothesis.

Decision based on the P-value method:

• If P-value < α, then reject H₀.
• If P-value ≥ α, then fail to reject H₀.