Relation between Confidence Intervals and Hypothesis Tests

Confidence intervals is used to estimate the population parameters as a function of "number of standard deviations away from the mean".

For example:
When we use z-statistic and with 95% confidence that our interval will include the population mean (μ), the interval is:

(-1.96)(standard error) < (sample mean) < (+1.96)(standard error).

Hypothesis tests is used to test the value of population parameters, either reject or not reject based on "number of standard deviations away from the mean".

For example:
To test the null hypothesis at the 5% significance level and use the z-statistic, not reject H0 if:

(-1.96)(standard error) < (sample mean) – (hypothesis population mean) < (+1.96)(standard error).

In Hypothesis testing, an interval within which the null will not be rejected is created, and we are 95% confident in this interval (i.e. there's a 5% chance of a type I error).