Question

Hypothesis testing is based on the idea that if there is enough of a difference between your experimental sample and the comparison distribution, you can see the research supports your hypothesis.

Describe an experiment in which you would expect there to be a very small difference between the experimental sample and the comparison distribution. How small of a difference could there be for you to still be okay with rejecting the null hypothesis?

Answer 1

Example of Hypothesis testing:

In a pipe manufacturing facility, the manager must ensure that the diameters of its pipes are equal to 5cm. For this, he does the Hypothesis testing using the following basic steps:

1. Specify the hypotheses.
Manager assumes the null hypothesis as "Population means of all the pipes equal to 5 cm (H0: μ = 5)".

So he chooses from the following category of alternative hypotheses:

Condition to test	Alternative Hypothesis
Population means is less than the target. one-sided:	μ < 5
Population means is greater than the target. one-sided:	μ > 5
Population means differs from the target. two-sided:	μ ≠ 5

Since they need to ensure that the pipes are not larger or smaller than 5 cm, so the manager chooses the two-sided alternative hypothesis, which states that the population mean of all the pipes is not equal to 5 cm (H1: μ ≠ 5)

2. Choose a significance level (α).
The manager selects a significance level of 0.05, which is the most commonly used significance level.

3. Collect the data.
They collected a sample of pipes and measured their diameters.

4. Compare p-value from the test with the significance level.
After performing the hypothesis test, the manager obtains a p-value of 0.004 which is less than the significance level of 0.05.

5. Now Decide whether to reject or fail to reject the null hypothesis.
The manager rejects the null hypothesis and comes to the conclusion that the mean diameter of all pipes is not equal to 5cm.

As we know that the decision to reject the null hypothesis (H0) can be based on the p-value and chosen significance level (also called α). If the p-value is less than or equal to α, you reject H0, else you fail to reject H0.

Also, the decision can be based on the confidence interval calculated using the same α as:

• If the reference value specified in H0 lies outside the interval, you can reject H0.
• If the reference value specified in H0 lies within the interval, you fail to reject H0.