Statistical Hypothesis Testing, an assumption regarding a population parameter is referred to as a statistical hypothesis.

For example, we can assume that the average male height in India is 60 inches. The statistical hypothesis is the height assumption, and the population parameter is the true mean height of a male in India.

A hypothesis test is a formal statistical test that we employ to determine whether a statistical hypothesis should be rejected or not.

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## Statistical Hypothesis Testing in Two Forms

We take a random sample from the population and run a hypothesis test on the sample data to see if a statistical hypothesis about a population parameter is correct.

Statistical hypotheses can be divided into two categories:

**The null hypothesis**, abbreviated as H0, states that the sample data is entirely due to chance.

**The alternative hypothesis**, often known as H1 or Ha, is that the sample data is impacted by a non-random cause.

### Statistical Hypothesis Testing

There are five steps to a hypothesis test:

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#### 1. Outline your hypotheses.

The null and alternative hypotheses should be stated. These two theories must be mutually exclusive, which means that if one is correct, the other must be incorrect.

#### 2. Decide on a significance level for the hypothesis to be tested.

Decide on a level of significance. The most common values are 0.01, 0.05, and 0.1.

#### 3. Figure out what the test statistic is.

Find the test statistic and the p-value for it. When analyzing a population mean or proportion, the general formula for determining the test statistic is:

(sample statistic – population parameter) / (standard deviation of statistic)

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#### 4. Reject the null hypothesis or fail to reject it.

Determine if you can reject or fail to reject the null hypothesis based on the significance level using the test statistic or the p-value.

The p-value indicates how strong the evidence is in favor of a null hypothesis. We reject the null hypothesis if the p-value is less than the significance level (Common cases <=0.05).

#### 5. Analyze the outcomes.

In the context of the question being posed, interpret the hypothesis test results.

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## Decision Errors in Two Forms

When performing a hypothesis test, there are two sorts of choice errors that might occur:

When you make a **Type I error**, you reject the null hypothesis even when it is correct. The likelihood of making a Type I error is equal to the significance level, often known as alpha, and indicated as α.

When you make a **Type II error**, you fail to reject the null hypothesis even when it is untrue. The **Power of the Test or Beta**, given as is the probability of making a Type II error.

### Tests with one and two tails

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There are two types of statistical hypotheses: **one-tailed and two-tailed.**

Making a “greater than” or “less than” declaration is part of a one-tailed hypothesis. Assume that the average height of a guy in India is greater than or equal to 60 inches.

H0: ≥ 60 inches would be the null hypothesis, and H1: < 60 inches would be the alternative hypothesis.

Making an “equal to” or “not equal to” declaration is part of a two-tailed hypothesis. Let’s say we assume a male’s average height in India is 60 inches.

H0: = 60 inches would be the null hypothesis, while H1:≠ 60 inches would be the alternative hypothesis.

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