Question

Example (from 8-1)
Someone claims that the mean height of men is equal to 174.1cm, against which a hypothesis test is to be
conducted.
1. What is the null hypothesis, and how is it denoted?

2. What is the alternative hypothesis, and how is it denoted?

3. You found a sample from which the sample mean of men’s heights was 175 cm. You suspect that the
actual mean height of men is greater than 174.1 cm. What is the alternative hypothesis here? How is it
denoted?

4. Your friend found another sample from which the sample mean of men’s heights was 173.9 cm. You
suspect that the actual mean height of men is less than 174.1 cm. What is the alternative hypothesis here?
How is it denoted?

5. What are the possible conclusions that can be made about the null hypothesis?

6. Someone concluded that there is sufficient evidence to support the claim that the mean height of men is
equal to 174.1cm. What would be your response?

Answer 1

1. What is the null hypothesis, and how is it denoted?

Null hypothesis always has an equal sign and the claim is mean is equal to 174.1 so it is denoted as:

2.As it is asked to check whether mean is equal to 174.1 or not so it is a two tailed test and alternate hypothesis is denoted as;

3. You found a sample from which the sample mean of men’s heights was 175 cm. You suspect that the
actual mean height of men is greater than 174.1 cm. What is the alternative hypothesis here? How is it
denoted?

As it is claimed that actual mean height of men is greater than mean so it would be a single tailed test and would be denoted as

4. Your friend found another sample from which the sample mean of men’s heights was 173.9 cm. You
suspect that the actual mean height of men is less than 174.1 cm. What is the alternative hypothesis here?
How is it denoted?

Here it it claimed that mean of men's heights is less than 174.1 so it is also a single tailed test and denoted as

5.Here we need to test the hypothesis and find the P-value.If the P-value is less than alpha we reject the null hypothesis i.e. actual mean is not 174.1 and we will support alternate hypothesis and claim will be supported while if P-value is greater than alpha we will fail to reject the null hypothesis that means we do not have sufficient evidence to support the claim that is alternate hypothesis.

6. Someone concluded that there is sufficient evidence to support the claim that the mean height of men is
equal to 174.1cm. What would be your response?

If the P-value is greater than alpha we fail to reject the null hypothesis.That means that the average height is equal to 174.1.The greater the P-value the power of the test will be greater and the support will be stronger that the mean height is 174.1 and viceversa.