A one-tailed test is a statistical test in which the null hypothesis is that the population mean is less than or equal to the value specified in the alternative hypothesis. A one-tailed test is also known as a directional test.

Why is a one tailed test more powerful? A one tailed test is more powerful than a two tailed test because it allows you to test for a specific hypothesis. For example, if you want to test whether a stock is underpriced, you would use a one tailed test. This is because you are looking for a specific result (the stock is underpriced) and not just any result that is statistically significant.

### What is one tailed p value?

One tailed p value is a statistical measure that is used to assess the likelihood that a given observation is due to chance. It is calculated by dividing the number of observations in a given sample that are greater than or equal to the observed value by the total number of observations in the sample. The resulting p value can then be compared to a predetermined significance level (usually 0.05) to determine whether or not the observed value is statistically significant.

##### What is the difference between 1 tailed and 2 tailed tests in terms of the critical regions?

When conducting a hypothesis test, you need to define the critical region, which is the set of values of the test statistic that would lead you to reject the null hypothesis. The critical region can be either one-tailed or two-tailed.

A one-tailed test is used when you are interested in testing whether a parameter is greater than or less than a specific value. For example, you might want to test whether the mean of a population is greater than 10. In this case, the critical region would be values of the test statistic that are either very large (if you are testing for a mean greater than 10) or very small (if you are testing for a mean less than 10).

A two-tailed test is used when you are interested in testing whether a parameter is significantly different from a specific value. For example, you might want to test whether the mean of a population is significantly different from 10. In this case, the critical region would be values of the test statistic that are either very large or very small.

#### What are the different tail tests?

There are a few different types of tail tests that are commonly used. The first is the one-tail test, which is used to test for a specific direction of a difference. For example, a one-tail test could be used to test whether a stock price is higher than it was a year ago. The second type of tail test is the two-tail test, which is used to test for a difference in either direction. For example, a two-tail test could be used to test whether a stock price is different than it was a year ago. The third type of tail test is the signed-rank test, which is used to test for a specific direction of a difference while taking into account the magnitude of the difference. For example, a signed-rank test could be used to test whether a stock price is higher by a certain percentage than it was a year ago. What is a one tailed confidence interval? A one tailed confidence interval is an interval estimate of a population parameter that is constructed so that the probability that the population parameter falls within the interval is equal to the desired confidence level. The desired confidence level is typically 95% or 99%.

For example, suppose we want to construct a 95% confidence interval for the population mean. We would do this by finding the values that bounds the central 95% of the distribution of the sample means. This means that we would find the values that correspond to the 2.5th and 97.5th percentiles of the distribution of the sample means. The resulting interval would be our 95% confidence interval for the population mean.

It's important to note that a one tailed confidence interval is different from a one tailed hypothesis test. A one tailed hypothesis test is used to test whether a population parameter is significantly different from a specific value, whereas a one tailed confidence interval is used to estimate the value of a population parameter.