Question

Explain in detail the difference between the null hypothesis and alternative Hypothesis.

In what cases you reject the Null and apply the alternative give a practical example.

Answer 1

Answer)

Null hypothesis Ho means no difference, while alternate hypothesis is research hypothesis and is used as claim most of the times

For example

Lets say in 2015, average score out of 100 in maths of students was 70

Now teacher wants to test if score has been increased

Suppose from previous records it is known that population standard deviation is 10

So, null hypothesis Ho : u = 70 (that is no difference)

Alternate hypothesis Ha : u > 70 (thats what the claim is)

Teacher took a random sample of 36 students and found the average score of 75

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (75 - 70)/(10/√36) = 3

From z table, P(z>3) = 0.0013

As the population s.d is given here so we used z table

If given significance level is 0.05 (which is most widely used)

We will reject the null hypothesis as 0.0013 is < 0.05

So alternate would be accepted that score has been increased