** 1. Introduction to Hypothesis Testing**

A hypothesis, in statistics, is a statement about a population where this statement typically is represented by some specific numerical value.

## 2. **Types of Hypotheses**

Hypothesis testing is formulated in terms of two hypotheses:

- H
_{0}: the null hypothesis - H
_{1}: the alternative hypothesis.

**3. Steps for Testing the Hypothesis**

In hypothesis testing there are certain steps must follow. Below these are summarized into six such steps to conduct a test of a hypothesis.

**Step 1.** **Setting up two competing hypotheses** – Each hypothesis test includes two hypotheses about the population. One is the null hypothesis, notated as H_{0} and the second hypothesis is called the alternative hypothesis, notated as H_{1}. (Write Null and Alternative Hypothesis)

**Step 2.** **Set some level of significance called alpha** **or confidence level called beta – **This value is used as a probability cut off for making decisions about the null hypothesis. (Find Confidence level or Significance level)

Type I Error : Rejecting Null Hypothesis when it should be accepted (High value of Significance Level ‘α’).

Type II Error : Accepting Null Hypothesis when it should be rejected (High value of Confidence Level ‘β’).

**Step 3.** **Calculate a test statistic – **The test statistic is calculated under the assumption the null hypothesis is true, and incorporates a measure of standard error and assumptions (conditions) related to the sampling distribution. (Find standard error of mean)

**Step 4. Decide type of Distribution –** Calculate Z-distribution or T-distribution.

Z- Confidence Level

T- Significance Level + Degree of Freedom

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. The number of independent ways by which a dynamic system can move, without violating any constraint imposed on it, is called number of degrees of freedom. It is denoted by df.

Where, n is the number of variables in the series in a row or column.

**Step 5.** **Calculate probability value (p-value), or find rejection region** – A p-value is found by using the test statistic to calculate the probability of the sample data producing such a test statistic or one more extreme. The rejection region is found by using alpha to find a critical value; the rejection region is the area that is more extreme than the critical value.

- P-value is less than significance level -> reject H
_{0} - P-value is greater than significance level -> fail to reject H
_{0 }What is “significance level” - Arbitrary (but strategic) choice by investigator
- Often 0.05 (or 0.10 or 0.01)

**Step 6.** **Make a decision and State an overall conclusion** – We decide to either reject the null hypothesis or fail to reject the null hypothesis. Once we have found the p-value or rejection region, and made a statistical decision about the null hypothesis (i.e. we will reject the null or fail to reject the null). Following this decision, we want to summarize our results into an overall conclusion for our test.

The end result of a hypothesis testing procedure is a choice of one of the following two possible conclusions:

- Reject H
_{0}(and therefore accept H_{1}), or - Fail to reject H
_{0 }(and therefore fail to accept H_{1}).

## 4. **Probability Curve of Sampling Distribution**

**References:**

- https://onlinecourses.science.psu.edu/stat500/node/39
- http://isites.harvard.edu/fs/docs/icb.topic129780.files/Lecture_4/Evans_lecture4.pdf

**About Suman Maity:**

Suman Maity is a B.Tech(Electrical Engineering) . Currently he is working as an Analyst Intern with NikhilGuru Consulting Analytics Service LLP, Bangalore. He has prior worked for around 1+ year with T&M Services Consulting Pvt Ltd and HR Chamber Outsourcing Pvt Ltd.

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