One Tailed Test Definition Hypothesis Example P Value

One-Tailed Test Definition

The determination of this test cannot be ambiguous, meaning that it can be either less or more than the population mean but cannot be both. Hypothesis testing determines the probability of a hypothesis being correct. The test validates the accuracy of the alternate hypothesis by eliminating randomness.

Key Takeaways

For a one tailed test hypothesis, the sample mean value can be either more or less than the population mean value but cannot be both. The null hypothesis and alternative hypothesis precede one-tailed tests—along with a p-value (probability value). The test is directional; hence it does not consider the other direction while establishing a relationship.

One Tailed Test Explained

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The one tailed test is a statistical method of hypothesis testing. Based on statistical data, hypothesis testing determines whether a theory is true or not. If a test shows the mean sample being both larger and smaller than the population, it is a two-tailed test. But when a test shows the sample mean being only larger or smaller than the population, it is a one tailed test. So, during testing, if sample data predominantly occur on one side, then the null hypothesisNull HypothesisNull hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption.read more will be rejected—an alternate hypothesis would be accepted.

One-tailed tests are preceded by the null hypothesis and alternative hypothesis. Researchers are required to prove the null hypothesis wrong; only then can they claim the alternative hypothesis. Ideally, in order to prove a theory, researchers need to eliminate randomness. When they prove an observation caused by a specific cause, the observations should not be caused by random factors. Randomness levels are determined by statistical significanceStatistical SignificanceStatistical significance is the probability of an observation not being caused by a sampling error.read more.

A significance level is represented as “p,” referring to probability. Usually, significance values are either 1%, 5%, or 10%. However, researchers have the discretion to use any other probability. The probability value is calculated assuming that the null hypothesis is true. The lower the p-valueP-valueP-Value, or Probability Value, is the deciding factor on the null hypothesis for the probability of an assumed result to be true, being accepted or rejected, & acceptance of an alternative result in case of the assumed results rejection. read more, the lesser the randomness—the null hypothesis will easily be proven false. If the resulting p-value is below 5%, the difference between both observations is statistically significant, and the null hypothesis is rejected.

Example

Let us understand the application of one-tailed tests with an example.

Let us assume a school principal wants to prove that a new math professor increased classroom performance by 9.29%. The principal set up the null (H0) and alternative (Ha) hypotheses:

H0: μ ≤ 9.29

Ha: μ > 9.29

The principal hopes to reject the null hypothesis and validate his claim as the alternative hypothesis. If the test rejects the null hypothesis, the alternative hypothesis is supported. On the contrary, if the test outcome fails to reject the null hypothesis, the principal will have to research further to discover other explanations for the classroom performance.

The rejection region lies on one side of the sampling distributionSampling DistributionA sampling distribution is a probability distribution using statistics by first choosing a particular population and then using random samples drawn from the population. It targets the spreading of the frequencies related to the spread of various outcomes or results which can take place for the particular chosen population.read more. Therefore, to determine how the classroom performed compared to a different mathematics professor, the principal must run a right-tailed significance test—extreme values must fall on the right side of the normal distribution curve. A normal distributionNormal DistributionNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more or Gaussian distribution refers to a probability distribution where the values of a random variable are distributed symmetrically. These values are equally distributed on the left and the right side of the central tendencyCentral TendencyCentral Tendency is a statistical measure that displays the centre point of the entire Data Distribution & you can find it using 3 different measures, i.e., Mean, Median, & Mode.read more. Thus, a bell-shaped curve is formed.

The one tail test results, represented in the right-tail curve area could show an overlap between increased classroom performance and the period taught by the new professor. Further, the test will show if the results were significantly different for the previous professor.

One Tailed Test Definition Hypothesis Example P Value