We always use this word, ‘hypothetical’ in multiple contexts in which we come up with an imaginary or a real-world problem and arrive at a solution by taking in multiple factors affecting that problem. When it comes to sports, we often knowingly or unknowingly talk a lot about hypotheses, where we either try and predict a team’s score or a player’s current form.

Rohit Sharma has been India’s backbone for the past 10 years and has been their most consistent opener since then. But there has been a decline in the consistency of his performances ever since the England series in 2021. His long list of injuries is also a factor in his declining performance, but India would definitely want him to regain his form with the world cup on its way.

### Hypothesis Testing

Let us have a statistical take on Rohit’s performance in the ODIs using the concept of Hypothesis Testing. This blog tends to get a bit technical but we have tried our best to explain in simple words. Hypothesis Testing refers to a statistical technique which is used to investigate our ideas or theories by using data. There are two types of hypotheses we use in this testing.

• Null Hypothesis: This is the theory or hypothesis that is going to be tested on whether it’s true or not. Our Null Hypothesis is – ‘Rohit Sharma is an In-Form batter’. Statisticians usually try to reject the null hypothesis and they accordingly formulate statements.
• Alternate Hypothesis: This covers everything else that is not covered by the Null Hypothesis and Statisticians usually try to accept the alternate hypothesis. Our Alternate Hypothesis is –  Rohit Sharma is not an In-Form batter’.

In order to conduct the hypothesis testing, we have 2 different methods, The Z-test and the T-test. We usually use the T-test when we don’t have the value of population variance (i.e: the variance in the overall population data) and we usually use the T-test if we have a sample population size of less than 30. Since we are considering only the last 10 ODI’s of Rohit’s career and since we don’t know the population variance (ie; variance of all his scores in ODI), we can use the T-test method.

We also have a term called significance level (alpha) which determines the probability that we reject the null hypothesis and this value is usually 0.05 which is considered to be a rule of thumb. Once we have determined this value, we have something called the T table from which we have to find the value corresponding to the number of samples and significance level considered. Using the table, we find out that the value is 1.833.

### T-test Implementation

Now, we use a T-test statistic and the formula is given below. Here, X̄: sample mean, µ: population mean, S: sample standard deviation, n: number of sample size.