Null Hypothesis: Overview, Questions, Preparation

This chapter has multiple topics listed below:

Statistics Standard Deviation Correlation Bar Graph Chi Square Test Measures of Central Tendency Variance Extrapolation Null Hypothesis Pareto Chart Harmonic Mean How to find Median Statistics Definition Data Collection Methods Frequency Polygons Central Tendency Confidence Interval Data Handling Statistical Inference Quota Sampling Interquartile Range Quartiles Variance and Standard deviation Cluster Analysis Correlation and Regression Graphical Representation Least Square Method Level of Significance Paired T Test Z Score Table Assumed Mean Method Box and Whisker Plot Gamma Distribution Sample Size T Distribution Tests of Significance Types of Statistics Continuous Variable Sample Statistic Exponential Smoothing T Test Table Bivariate Analysis Relative Frequency Difference between Average and ...Difference between Mean and Med...Difference between Parametric a...Grouping data Statistics pdf Mean Absolute Deviation Population and Sample

Rachit Kumar SaxenaManager-Editorial

Updated on Aug 13, 2021 14:11 IST

Table of Contents

What is Null Hypothesis ?
Weightage of Null Hypothesis
Illustrative Examples of Null hypothesis
FAQs on Null hypothesis

What is Null Hypothesis ?

A hypothesis that no distinction between conditions or no relationship between variables would be identified by an experiment. It can be characterized as a hypothesis where two variables in the hypothesis have no statistical significance. The general presumption is that the null hypothesis is correct, and the same can not be disputed until any required results or analysis is given in support of it.

Explanation

In the world around you, a hypothesis is a guess about something. It should, either by experiment or observation, be testable. For instance:

A modern medication.
For greater understanding, a way of teaching.

Null Hypothesis?

In simpler terms, the null hypothesis is always the truth that everyone has embraced. Easy examples of null hypotheses commonly accepted as true are the following:
In the solar system, only one sun exists.

H0 is expressed as the null hypothesis, which is pronounced as H-nought, H-null, or H-zero. The opposite of the null hypothesis is an alternate hypothesis.

Principle
The principle for the null hypothesis is that we collect the data and frame the hypothesis according to the dataset collected. Later we assume the hypothesis to be true.

The formula for the null hypothesis

H0: p = p0

Weightage of Null Hypothesis

The null hypothesis is a topic under statistics, which carries 11 marks weightage in Class 10th and Class 11th, statistics and probability jointly carry 10 marks.

Illustrative Examples of Null hypothesis

1. The hardness of 24 pieces of ductile iron was tested by an engineer. The data resulting from this was:
170 166 173 178 178 185 173 187 173
155 162 154 186 155 166 157 175
182 178 175 177 170 158 186.
The engineer hypothesized that all such ductile iron bits have an overall hardness of greater than 172. What would be the assumption?

Solution:

H0: μ = 172 HA: μ > 172 HA: μ > 172 Solution:

The hardness of ductile iron parts would be equal to 172 if the null hypothesis says. He is going to test the knowledge and conclude accordingly.

2. A biology student was evaluating whether certain seedlings treated with an extract from minor roots results in a lower average height of seedlings than the normal height of 15.6 cm. A random sample of n = 30 seedlings were found, and the following heights were subsequently obtained:
11.4 11.7 15.6 16.2 14.2 10.7 9.4 15.0
15.1 19.1 12.6 12.3 19.1 13.4 12.3 13.3
16.4 13.4 14.5 16.5 10.8 13.1 10.4
15.2 17.2 13.4 12.3 8.6 14.4 12.8

Solution:

The hypothesis can be stated as follows-
H0 : μ = 15.6
HA : μ

3. A researcher is researching the effects on back surgery patients of exercise programs. For knee surgery patients, the estimated recovery time is 8.4 weeks. What's the null hypothesis here?
Solution:
The null hypothesis states that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.4 weeks.
H0: μ = 8.2

FAQs on Null hypothesis

Q: What is the p-value?

A: The p-value is conditional on the true null hypothesis being unrelated to the test hypothesis' validity or falsity. A p-value greater than 0.05 (> 0.05) is not statistically relevant, and the null hypothesis provides clear evidence.

Q: When is a null hypothesis rejected?

A: Typically, the null hypothesis is dismissed using the P-value principle method. The null hypothesis can be discarded if the P-value is less than or equal to the alpha, and the findings are in favor of the alternative hypothesis.

Q: What is an alternative hypothesis?

A: Alternative hypothesis: a declaration claiming that two observable phenomena or variables have some relationship. The results of this theory are presumed to be the product of some real effect.

Q: What are the different types of the null hypothesis?

The following are the major types of null hypothesis:

Simple hypothesis
Exact hypothesis
Inexact hypothesis
Composite hypothesis

Q: What is the main advantage of hypothesis testing?

A: Hypothesis testing is regarded as a type of inferential statistics, which allows the whole population to draw conclusions based on a representative sample.