Accept me or Reject me- I am your ‘Hypothesis’
#Data Science
Sarvesh Kumar Yadav
July 5, 2021
Hypothesis:
Hypothesis is an assumption which is made based on few evidences. It is called a hypothesis because it is not known whether it is True or False.
“An hypothesis Test is standard procedure for testing a claim about a population”
E.g: ‘Women multitask better than men’
‘Men Parallel park better than woman’
Rare Events:
Events which have very low probability under given assumptions are called ‘Rare Events’. In this case, assumptions are probably not True.
Components of a Hypothesis-Test:
- Null Hypothesis
- Alternate Hypothesis
- Test Statistics
- Critical Values
- p-values
- Conclusion
Test Statistics:
Test statistics is a value used in making a decision about the Null Hypothesis.
It is calculated by converting the sample statistics to a score, with an assumption that Null Hypothesis is True.
Critical Values:
Critical values are the cut off values, where the test statistics is unlikely to lie.
p-values:
p-value is probability of test statistics being as extreme as possible, when Null hypothesis is true.
- -> p-value is higher , Null Hypothesis is accepted.
- -> p-value is lower, Null Hypothesis is rejected.
Conclusion:
It is summary that whether the Null Hypothesis is accepted or rejected. Based on this we take final decision.
Ex1:
The average IQ of a sample of 50 university students was found to be 105. Carry out a statistical test to determine whether the average IQ of university students is greater than 100, assuming that IQs are normally distributed. It is known from previous studies that the standard deviation of IQs among students is approximately 20.
Solution:
Test Statistics:
For determining the test statistics, first thing to choose is the Probability Distribution type.
All type of distribution has different formulae. It is necessary to choose correct distribution to get correct result.
Different types of test statistics are as below:
Same approach is used for Hypothesis testing, Where we decide type of test right tail or left tail, then we will check for significance level.
In case of two tail test, it is same up to 2.5% from left and 2.5% from right for 5% level of significance. Critical values are z=-/+ 1.96
For, Right tail Null hypothesis value should below=1.65. Null is accepted
For, Left tail Null Hypothesis value should lie above = -1.65. Null is accepted.
Type-I Error and Type-II Error:
Power of Hypothesis Test:
Power of Hypothesis test is a probability(1-ß) of rejecting a Null Hypothesis when it is false . It is probability of not making a type-II kind of Error.
Solved Examples:
Q1: Carry out a statistical test to assess whether the standard deviation of the heights of 10- year-old children is equal to 3cm, based on the random sample of 5 heights in cm given below. Assume that heights are normally distributed.
124, 122, 130, 125, 132
Solution:
