# 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 (H0 = 90).
: Battery life has increased (H1) > 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 tcrit from a table compiled for a two-tailed t-test at the desired confidence level. For example, the critical value tcrit at the 95% confidence level for ν = 7 is t7,95% = 2.36. Since in this case t is greater than t7,95%, 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 HA: μold μnew. 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:

### FAQ: What are the differences between one-tailed and two-tailed tests

The complete table of critical values of Z for upper, lower and two-tailed tests can be found in the table of Z values to the right in "Other Resources."

### Will That be One Tail or Two? - Actual Analysis

This is another example of a one-tailed test. The null hypothesis says that the average amount of cola in the bottle is 1 liter over all the bottles that Liter O'Cola makes. The alternative is that maybe we think that it's less than 1. They're under-filling the bottles. The average amount is less than 1 liter.

### The Difference Between One-Tailed & Two ..

Most tables of critical t-values give you values for either a one- or two-tailed test, but not both. Because of this, you will need to know how to use one-tailed tables for two-tailed tests, and vice versa. The conversion is actually quite simple. As , a on-tailed test at the 95% confidence level uses the same point on the value axis of the population distribution as a two-tailed test at the 90% confidence level. Similarly, a one-tailed test at the 90% confidence level uses the same criterion as a two-tailed test at the 80% confidence level: