Q: When to use hypothesis?

Assume an industrial company decides to start a project in a village. This would require the village people to relocate to other places. To compensate this, they offer rehabilitation and resettlement package to the affected village people. Now the hypothesis is used to answer, “will the industry win the confidence of the affected local people by the R&R package”.

For this a survey is conducted from 1000 villagers. asking questions if they accept the package. From these 550 villagers support this offer.

 set hypotheses:

• Null hypothesis (H₀): p = 0.5.
• Alternative hypothesis (H₁): p > 0.5

As the sample size is high (1,000 people), use the z-test for proportions, which takes that the data shows a normal distribution (Central Limit Theorem).

The z-value is calculated as 3.16 by the formula for the z-test of proportions.

Now, we compare this to the z score from the z-table for 0.01 significance level (1% probability for error), that is 2.33.

• The Z score 3.16 is higher the 0.01 significance level, so we reject the null hypothesis.
• The p-value is 0.0008, this means the probability of the result obtained by random chance is very less.

From the testing we can conclude that there is higher statistical evidence that more than half of the villagers support the package. So, we can state that the industrial house is more likely to win the confidence of the affected village people. [1]