Question

Single sample Hypothesis, Independent and Dependent Hypothesis

How do you identify the null and alternate hypothesis and their direction in terms of =, < and >?

Can I have a clear explanation with several examples

Answer 1

The null hypothesis always must have to contain the equal sign.

For eg. if it says, the mean distance traveled is 20 miles, it means the null hypothesis is H0: = 20 miles.

the alternative hypothesis is of three types.

(1) If it says the mean distance traveled is greater than 20 miles.

The null is H0: = 20 and the Alternative is Ha: > 20

The null has to have the equal to sign, and this would be a right tailed (one tailed) test.

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(2) If it says the mean distance traveled is lesser than 20 miles.

The null is H0: = 20 and the Alternative is Ha: < 20

This would be a left tailed (one tailed) test.

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(3) If it says the mean distance traveled is different than or not equal to 20 miles.

The null is H0: = 20 and the Alternative is Ha: 20

his would be a two tailed test.

Sometime they do not say anything about the direction and directly talk about the null hypothesis. Then in that case it may be assumed that we have to conduct a 2 tailed Hypothesis.

For eg. The mean distance traveled is 20 miles. A sample of 10 cars gave a mean of 18 miles, and a sd of 2 miles. Can we conclude that the claim is correct?. So here since only the null hypothesis is mentioned that H0: = 20, therefore we can assume that the alternative is Ha: 20 (as direction lesser than or greater than is not given)

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Sometimes the questions can come with terms like at least and at most. At means means greater than or equal to , and at most means lesser than or equal to (). At least and at most are for one tailed tests only, because these will be part of the null hypothesis and its opposite sign will be part of the alternative hypothesis

Eg1. The birth of premature babies is known to be at most 10 kgs. A doctor thinks otherwise and wants to test it (it means he disagrees about at most i.e lesser than or equal to and thinks it is greater than what is mentioned).

Therefore the Hypothesis is

H0.   10 (As stated, the null has to have the equality sign. the alternative cannot have the sign of equality in any form)

Ha: > 10

Eg2. The birth of healthy babies is known to be at least 12 kgs. A doctor thinks otherwise and wants to test it. (it means he disagrees about at least i.e greater than or equal to and thinks it is lesser than what is mentioned).

Therefore the Hypothesis is

H0.   10 (As stated, the null has to have the equality sign. the alternative cannot have the sign of equality in any form)

Ha: < 12

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Hope this helps