In the world of statistics, we rarely deal with absolute certainties. Instead, we deal with “claims.” A pharmaceutical company claims a drug is 90% effective; a manufacturer claims their lightbulbs last 2,000 hours; a politician claims 60% of the public supports a new policy. Tests of Hypothesis is the formal, mathematical process we use to decide whether these claims hold water or if they are simply the result of random chance. For students, this unit is the heart of inferential statistics and a major component of any rigorous academic sitting.
Below is the exam paper download link
PDF Past Paper On Tests Of Hypothesis For Revision
Above is the exam paper download link
To help you move from “guessing” to “proving,” we have structured this revision guide around the core logical hurdles found in recent past papers.
What is the “Null Hypothesis” ($H_0$) and why do we assume it’s true?
The Null Hypothesis is the “status quo.” It is the assumption that nothing has changed, or that there is no effect. For example, if you are testing a new fertilizer, your $H_0$ would be: “The new fertilizer has the same yield as the old one.” We assume $H_0$ is true until we find “overwhelming evidence” to the contrary. In an exam, always state your $H_0$ using an equals sign ($=$) to represent this baseline of no change.
How do we define the “Alternative Hypothesis” ($H_1$)?
The Alternative Hypothesis is what you are actually trying to prove. It is the “challenger” to the status quo. Depending on your research question, $H_1$ can be:
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One-Tailed (Left): You believe the value has decreased ($<$).
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One-Tailed (Right): You believe the value has increased ($>$).
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Two-Tailed: You just believe the value has changed, but you aren’t sure in which direction ($\neq$).
What are Type I and Type II Errors?
This is a classic “trap” question in almost every statistics exam.
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Type I Error ($\alpha$): This is a “False Alarm.” It happens when you reject a Null Hypothesis that was actually true. In the legal world, this is like convicting an innocent person.
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Type II Error ($\beta$): This is a “Miss.” It happens when you fail to reject a Null Hypothesis that was actually false. This is like letting a guilty person go free.
The “Significance Level” (usually 0.05 or 5%) is the probability you are willing to accept for making a Type I Error.
How do we choose between a Z-test and a T-test?
This choice determines the accuracy of your entire calculation.
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Z-test: Use this if your sample size is large ($n > 30$) OR if you already know the population standard deviation ($\sigma$).
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T-test: Use this if your sample size is small ($n < 30$) AND you only have the sample standard deviation ($s$).
In a revision context, mastering the “Degrees of Freedom” ($n – 1$) for the T-test is vital for looking up the correct critical value in your statistical tables.
What is the “P-value” and how does it lead to a decision?
The P-value is the probability of getting your observed result (or something more extreme) if the Null Hypothesis is true. It is the “Ultimate Decider.”
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If P-value $\leq \alpha$: Your result is “Statistically Significant.” You Reject $H_0$.
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If P-value $> \alpha$: Your result is not significant. You Fail to Reject $H_0$.
Think of it this way: A tiny P-value means the outcome was so unlikely to happen by chance that the “Status Quo” ($H_0$) must be wrong.
Why do we use “Chi-Square Tests”?
While Z and T tests compare means, the Chi-Square Test is used for categorical data. It helps us determine “Goodness of Fit” (does our data match a specific distribution?) or “Independence” (are two variables, like gender and voting preference, related?). If the “Observed” values are very different from the “Expected” values, the Chi-Square statistic will be large, leading you to reject the idea that the variables are independent.
Conclusion
Tests of Hypothesis is about building a legal case using numbers. You start with a premise, collect evidence (data), calculate a test statistic, and reach a verdict. Success in your finals comes from recognizing the “context” of the question—are you comparing two means, testing a proportion, or looking for a correlation?
To sharpen your logic and practice your decision-making, we have provided a link to a comprehensive past paper below.
Last updated on: March 24, 2026