Hypothesis and Its Types with Easy Examples

What is Hypothesis:
In statistics, a hypothesis is a clear, formal statement that explains how two or more variables are related in a specific population. It's like making an educated guess that helps researchers turn a problem into a straightforward prediction or explanation of what they expect to find in their study. A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis.
How do We Write statistics?
Steps :
Step 1:
Specify the Null Hypothesis.
Step 2:
Specify the Alternative Hypothesis.
Step 3:
Set the Significance Level (a).
Step 4:
Calculate the Test Statistic and Corresponding P-Value.
Step 5:
Drawing a Conclusion.
Interpretation and Selecting significance:
The researcher defines the significance level before conducting the experiment. 
The significance level is the probability of rejecting the null hypothesis when it is true.
Example:
For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
Types of Hypothesis:
Null Hypothesis and Alternative hypothesis. The null hypothesis is a way of saying, "There is no real effect or connection between the things we are studying." It's like assuming everything is just random and there's no special relationship between the groups or events we are looking at. Scientists use this idea to test whether something is truly happening or if it's just a coincidence.on the other hand The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test.
The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect, such as zero. The alternate hypothesis is just an alternative to the null. 
Examples:
 It’s an accepted fact that ethanol boils at 173.1°F; you have a theory that ethanol has a different boiling point, of over 174°F. The accepted fact (“ethanol boils at 173.1°F”) is the null hypothesis; your theory (“ethanol boils at temperatures of 174°F”) is the alternate hypothesis.
Types of Error:
There two type of error which exists that are:
Type 1 Error:
A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is true in the population. A Type I error (or Type 1), is the incorrect rejection of a true null hypothesis. The alpha symbol, α, is usually used to denote a Type I error.
Example: Type I error (false positive): the test result says you have coronavirus, but you actually don't.
Type 2 Error:
A type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is false in the population.
T-Test:
Two types of tests are involved :
One Tail Test and Two Tail Test

1. Hypothesis

2. What is Hypothesis In statistics, a hypothesis is a clear, formal statement that explains how two or more variables are related in a specific population. It's like making an educated guess that helps researchers turn a problem into a straightforward prediction or explanation of what they expect to find in their study . A statistical hypothesis test is a method of statistical inference used to decide whether the data at hand sufficiently support a particular hypothesis .

3. How do W e Write statistics? Steps : Step 1: Specify the Null Hypothesis. Step 2: Specify the Alternative Hypothesis .

4. Cont.. Step 3: Set the Significance Level (a). Step 4: Calculate the Test Statistic and Corresponding P-Value. Step 5: Drawing a Conclusion.

5. Interpretation and Selecting significance The researcher defines the significance level before conducting the experiment.  The significance level is the probability of rejecting the null hypothesis when it is true. Example: For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference .

6. Types of Hypothesis Null Hypothesis Alternative hypothesis

7. Null Hypothesis The null hypothesis is a way of saying, "There is no real effect or connection between the things we are studying." It's like assuming everything is just random and there's no special relationship between the groups or events we are looking at. Scientists use this idea to test whether something is truly happening or if it's just a coincidence.

8. Alternative H ypothesis The alternative hypothesis is one of two mutually exclusive hypotheses in a hypothesis test. The alternative hypothesis states that a population parameter does not equal a specified value. Typically, this value is the null hypothesis value associated with no effect, such as zero. The alternate hypothesis is just an alternative to the null. 

9. Examples   It’s an accepted fact that ethanol boils at 173.1°F; you have a theory that ethanol has a different boiling point, of over 174°F. The accepted fact (“ethanol boils at 173.1°F”) is the null hypothesis; your theory (“ethanol boils at temperatures of 174°F”) is the alternate hypothesis .

10. Types of Error There two type of error which exists that are : Type 1 Error: A type I error (false-positive) occurs if an investigator rejects a null hypothesis that is true in the population. A Type I error (or Type 1), is the incorrect rejection of a true null hypothesis. The alpha symbol, α, is usually used to denote a Type I error . Example: Type I error (false positive): the test result says you have coronavirus, but you actually don't.

11. Type 2 Error: A type II error (false-negative) occurs if the investigator fails to reject a null hypothesis that is false in the population. A Type II error (sometimes called a Type 2 error) is the failure to reject a false null hypothesis. The probability of a type II error is denoted by the beta symbol β . E xample: Type II error (false negative): the test result says you don't have coronavirus, but you actually do .

12. T-Test Two types of tests are involved : One Tail Test Two Tail Test

13. One Tail Test A one-tailed test is a statistical test in which the critical area of a distribution is one-sided so that it is either greater than or less than a certain value, but not both. If the sample being tested falls into the one-sided critical area, the alternative hypothesis will be accepted instead of the null hypothesis. A one-tailed test has the entire 5% of the alpha level in one tail (in either the left, or the right tail).  One-tailed tests allow for the possibility of an effect in one direction. 

14. Two Tail Test A two-tailed test splits your alpha level in half (as in the image to the left). Two-tailed tests test for the possibility of an effect in two directions—positive and negative. In statistics, a two-tailed test is a method in which the critical area of a distribution is two-sided and tests whether a sample is greater or less than a range of values. It is used in null-hypothesis testing and testing for statistical significance .

15. Example For example, let's say you were running a z test with an alpha level of 5% (0.05). In a one tailed test, the entire 5% would be in a single tail. But with a two tailed test, that 5% is split between the two tails, giving you 2.5% (0.025) in each tail.

16. Chi-Square Chi-square is a statistical test used to examine the differences between categorical variables from a random sample in order to judge goodness of fit between expected and observed results. A chi-square test is a statistical test used to compare observed results with expected results. The purpose of this test is to determine if a difference between observed data and expected data is due to chance, or if it is due to a relationship between the variables you are studying .

17. Formula

18. Fisher Test (z-test) Fisher's z' is used to find confidence intervals for both r and differences between correlations. But it's probably most commonly be used to test the significance of the difference between two correlation coefficients, r 1  and r 2  from independent samples. The Fisher Z transformation is a formula we can use to transform Pearson’s correlation coefficient (r) into a value (z r ) that can be used to calculate a confidence interval for Pearson’s correlation coefficient .

19. Formula The formula is as follows : z r  = ln((1+r) / (1-r)) / 2

20. THANK YOU!