Understanding Null and Alternate Hypothesis
Inferring Null and Alternate Hypothesis are quite confusing but it is first step in Hypothesis Testing. Wrong assumptions will lead to disasters in business world. Let’s understand the Null and Alternate Hypothesis with examples.
Before understanding, let’s learn few statistics terms, Population Mean, Sample Mean , Population variance and Sample variance.
Population Mean: Population Mean is defined as the mean for entire data.
Sample Mean: Sample Mean is defined as the mean of sample data.
Population Variance: Population Variance is defined as the variance for entire data.
Sample Variance: Sample Variance is defined as the variance for Sample data.
Hypothesis Testing means to make assumptions around population parameter using the data we have in our hand and perform statistical tests on data to make inference w.r.t assumptions.
Assumptions we make are two types, they are Null Hypothesis(H0) and Alternate Hypothesis(H1).
What are Null and Alternate Hypothesis Statements?
H0: The null hypothesis: It is a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion.
Ha: The alternative hypothesis: It is a claim about the population that is contradictory to H0 and what we conclude when we reject H0.
For example, let’s assume Average car sales is 1 million per year and opposite to previous statement is Average sales is not 1 million per year. After performing statistical test, we accept either one of the statements.
In the above example Null hypothesis is 1 million sales per year and Alternate hypothesis is not 1 million sales per year. From the results of statiscal tests, we decide whether to accept null hypothesis or accept alternate hypothesis.
We will learn about the statistical tests in another blog. Let’s understand how to infer Null Hypothesis and Alternate Hypothesis from the given data.
Mathematical symbols used for Null Hypothesis and Alternate Hypothesis:
Example 1 : Average Height of class is 5.5 feet with standard deviation of 0.55 feet. A sample of 10 students data is considered and average height of these 10 students is 5.2 feet. State Null and Alternate Hypothesis?
Here, the population mean is 5.5 feet because we considered the entire class but sample mean is 5.2 feet as it represents data of 10 students. Null hypothesis and Alternate Hypothesis will infer about Population data.
Example 2 : The train takes less than 50 minutes, on average to reach destination. State Null and Alternate Hypothesis?
Here, the data says train takes less than 50 minutes(<50) to reach destination and contradictory statement is train takes equal or more than 50 minutes (≥ 50).
Example 3 : A medical trial is conducted to test whether or not a new medicine increases antibodies atmost 25%. State the null and alternative hypotheses.
Here, the data says Antibodies increases by atmost 25%(≤0.25) with the new medicine and contradictory statement is affect due to medicine is more than 25%(>0.25).
Example 4 : Researchers report tells that 81 out of 100 mobile users still using 4GB ram. Sample of 12 users is collected and 7 out of 12 users using 4GB ram. State Null Hypothesis and Alternate Hypothesis.
From the report data, the 81 out of 100 using have mobiles with 4GB ram(=0.81) and contradictory to it is ≠0.81
Hope this blog helps you to understand on how to write Null and Alternate Hypothesis.
Thank you for reading. Please let me know if you have any feedback