# Statistical hypothesis

A statistical hypothesis is a statement about a population parameter. It is an educated guess about the value of the population parameter based on sample data. For example, one might hypothesize that the average height of adult women in the United States is 65 inches.

Typically, a statistical hypothesis test involves formulating two hypotheses about the population parameter and selecting the most appropriate hypothesis based on the sample data. The two hypotheses are:

• The null hypothesis, which states that there is no significant difference between the observed results and the expected results, or that there is no significant relationship between two measured phenomena.
• The alternative hypothesis, which states that there is a significant difference between the observed results and the expected results, or that there is a significant relationship between two measured phenomena.

Once the two hypotheses are formulated, a statistical test can be used to determine which hypothesis is the most plausible. The results of the test will indicate whether the null hypothesis or the alternative hypothesis is the better explanation of the observed results. If the null hypothesis is rejected, it implies that the alternative hypothesis is the correct explanation.

## Example of Statistical hypothesis

A statistician might formulate the following statistical hypothesis about the mean weight of adult men in the United States:

Null Hypothesis: The mean weight of adult men in the United States is 180 pounds.

Alternative Hypothesis: The mean weight of adult men in the United States is not 180 pounds.

In this example, the null hypothesis states that the mean weight of adult men in the United States is 180 pounds, while the alternative hypothesis states that the mean weight is not 180 pounds. A statistical test can be used to determine which of these hypotheses is the most plausible. If the null hypothesis is rejected, it implies that the alternative hypothesis is the correct explanation.

## When to use Statistical hypothesis

Statistical hypothesis tests are used to assess the plausibility of a hypothesis about a population parameter. This type of analysis is used when the data is too large or complex to analyze by hand. It is also used when the data is collected from a random sample of the population and the sample size is large enough that the results can be assumed to be representative of the population as a whole. Statistical hypothesis tests can also be used to compare two or more populations, or to determine if there is a relationship between two or more variables.

## Types of Statistical hypothesis

There are four main types of statistical hypothesis tests:

• The t-test is used to compare the means of two samples to determine whether they are significantly different from each other.
• The chi-square test is used to determine if two categorical variables are associated with each other.
• The F-test is used to compare the variances of two samples to determine if they are significantly different from each other.
• The ANOVA test is used to compare the means of three or more samples to determine if they are significantly different from each other.

## Steps of Statistical hypothesis

The steps for a statistical hypothesis test are:

• Step 1: State the null and alternative hypotheses.
• Step 2: Determine the level of significance.
• Step 3: Calculate the test statistic.
• Step 4: Compare the test statistic to the critical value and decide whether to reject or not reject the null hypothesis.

In step 1, the null and alternative hypotheses are stated in terms of the population parameter, such as the population mean or population proportion. In step 2, the level of significance, also known as the critical value, is determined. This is the probability of rejecting the null hypothesis when it is true. In step 3, the test statistic is calculated. This is the statistic that is used to compare the observed results to the expected results. In step 4, the test statistic is compared to the critical value and a decision is made whether to reject or not reject the null hypothesis.

There are several advantages of using statistical hypothesis testing. First, it allows researchers to draw conclusions from data that would otherwise be impossible to interpret. Second, it is a reliable and objective way to test hypotheses. Third, it is a cost-effective and efficient way to evaluate data and make decisions. Finally, it helps researchers to identify potential relationships between variables that may not be immediately apparent.

## Limitations of Statistical hypothesis

Statistical hypothesis tests do have their limitations. These include:

• They can only be used for hypothesis testing, not for making predictions about future data.
• The results of the tests are only as accurate as the assumptions used to formulate the hypotheses.
• The tests are only as good as the sample data that is used to test the hypotheses.
• The tests are limited by the level of precision that is used to calculate the test statistic.

## Other approaches related to Statistical hypothesis

In addition to the traditional approach of formulating two hypotheses, there are several other approaches that can be used when testing a statistical hypothesis. These approaches include:

• Fisher's exact test, which tests the hypothesis that two variables are independent.
• Chi-square test, which tests the hypothesis of no association between two variables.
• The t-test, which tests the hypothesis that two population means are equal.
• The F-test, which tests the hypothesis that two population variances are equal.
• The Z-test, which tests the hypothesis that a population mean is equal to a specified value.