Question

The accompanying data on degree of spirituality for a sample of natural scientists and a sample of social scientists working at research universities appeared in a paper. Assume that it is reasonable to regard these two samples as representative of natural and social scientists at research universities. Is there evidence that the spirituality category proportions are not the same for natural and social scientists? Test the relevant hypotheses using a significance level of 0.01.

	Degree of Spirituality
	Very	Moderate	Slightly	Not at All
Natural Scientists	58	157	193	215
Social Scientists	54	228	244	237

State the null and alternative hypotheses.

H₀: The spirituality category for natural scientists and social scientists are not independent.
H_a: The spirituality category for natural scientists and social scientists are independent.

H₀: The spirituality category proportions are the same for natural scientists and social scientists.
H_a: The spirituality category proportions are not all the same for natural scientists and social scientists.    

H₀: The spirituality category for natural scientists and social scientists are independent.
H_a: The spirituality category for natural scientists and social scientists are not independent.

H₀: The spirituality category proportions are not all the same for natural scientists and social scientists.
H_a: The spirituality category proportions are the same for natural scientists and social scientists.

Calculate the test statistic. (Round your answer to two decimal places.)
χ² =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

What can you conclude?

Do not reject H₀. There is not enough evidence to conclude that the spirituality category proportions are not all the same for natural scientists and social scientists.

Do not reject H₀. There is not enough evidence to conclude that there is an association between natural scientists and social scientists.    

Reject H₀. There is convincing evidence to conclude that there is an association between natural scientists and social scientists.

Reject H₀. There is convincing evidence to conclude that the spirituality category proportions are not all the same for natural scientists and social scientists.

Answer 1