Question

Describe how to write the null and alternative hypotheses based on a claim. Provide at least one example to clarify your explanation.(No plagiarism write in your own words)

Answer 1

Solution:

Let us start from some basic concepts in hypothesis testing .

Null hypothesis H₀ : The statement of " No difference"

Valid signs in H₀ : = or   or  

Alternative hypothesis H_a : The statement of " Significant difference" .It is complement of the null hypothesis.

Valid signs in H_a : or  <   or >

Suppose we are testing the mean

If our claim is " = 12 " versus " 12" then the hypothesis are

H₀ : =12 versus H_a : 12

If our claim is " mean is less than 12 ,then the hypothesis are

H₀ : = 12 versus H_a : < 12

If our claim is " mean is greater than 12 "   ,then the hypothesis are

H₀ : = 12 versus H_a : > 12

If our claim is " mean is at least 12 " or "Not less than 12" ,then the hypothesis are

H₀ :   12   versus H_a : < 12

If our claim is " mean is at most 12 " or "Not greater than 12" ,then the hypothesis are

H₀ :    12   versus H_a : > 12

Now , in testing the population proportion p , same rules .

In the given example , claim is  p>.50

So , the null and alternative hypothesis are

H₀ : p = 0.50 versus H_a : p > 0.50