# A one–tailed test uses an alternate hypothesis that states either:

One-tailed tests are preferred to two-tailed tests because they're more powerful. Statistical power means that they have a higher likelihood of actually detecting a difference if one is present. Let's take one last look visually at what a one-tailed test and a two-tailed test look like. This is what a one-tailed test with a p-value of 5% would look like.

## Rejection Region for Two-Tailed Z Test (H1: μ ≠ μ 0 ) with α =0.05

### This lesson will explain one-tailed and two-tailed tests.

A high-end computer manufacturer sets the retail cost of their computers based in the manufacturing cost, which is $1800. However, the company thinks there are hidden costs and that the cost to manufacture the computers is actually much more. The company randomly selects 40 computers from its facilities and finds that the mean cost to produce a computer is $1950 with a standard deviation of $500. Run a hypothesis test to see if this thought is true.

### A two-tailed test, here the normal distribution.

A right tailed test (sometimes called an upper test) is where your hypothesis statement contains a greater than (>) symbol. In other words, the inequality points to the right. For example, you might be comparing the life of batteries before and after a manufacturing change. If you want to know if the battery life is greater than the original (let’s say 90 hours), your hypothesis statements might be:

: No change (H_{0} = 90).

: Battery life has increased (H_{1}) > 90.

## Upper-tailed, Lower-tailed, Two-tailed Tests

We can either calculate the probability (*p*) of obtaining this value of *t* given our sample means and standard deviations, or we can look up the critical value *t _{crit}* from a table compiled for a two-tailed

*t*-test at the desired confidence level. For example, the critical value

*t*at the 95% confidence level for ν = 7 is

_{crit}*t*

_{7,95%}= 2.36. Since in this case

*t*is greater than

*t*

_{7,95%}, we can reject the null hypothesis and conclude that the pH values are significantly different at the 95% level of confidence.

## One and Two Tailed Tests - Mathematics A-Level Revision

One-tailed tests have two versions, a left-tailed test or a right-tailed test. A left tailed test is where you say in the alternative hypothesis that it's less than this claimed parameter. A right tailed test means that the alternative hypothesis is larger than the claimed parameter.

## What is one-tailed test and two-tailed test

We might be faced with a scenario in which a known source of contamination could *increase* the pH over time. In this case, we could use a one-tailed test to see if the stream indeed has a higher pH than one year ago. For this, we would use the alternate hypothesis *H*_{A}: *μ*_{old} *μ*_{new}. A more likely scenario, however, is that the pH could have increased, decreased, or stayed the same. As a result, we would want to use a more rigorous two-tailed test for the hypothesis that: