The accompanying data on degree of spirituality for a sample ofnatural scientists and a sample of social scientists working atresearch universities appeared in a paper. Assume that it isreasonable to regard these two samples as representative of naturaland social scientists at research universities. Is there evidencethat the spirituality category proportions are not the same fornatural and social scientists? Test the relevant hypotheses using asignificance level of 0.01.
| Degree of Spirituality |
|---|
| Very | Moderate | Slightly | Not atAll |
|---|
| NaturalScientists | 58 | 157 | 193 | 215 |
|---|
| SocialScientists | 54 | 228 | 244 | 237 |
|---|
State the null and alternative hypotheses.
H0: The spirituality category for naturalscientists and social scientists are not independent.
Ha: The spirituality category fornatural scientists and social scientists are independent.
H0: The spirituality category proportionsare the same for natural scientists and social scientists.
Ha: The spirituality categoryproportions are not all the same for natural scientists and socialscientists.
H0: The spirituality category for naturalscientists and social scientists are independent.
Ha: The spirituality category fornatural scientists and social scientists are not independent.
H0: The spirituality category proportionsare not all the same for natural scientists and socialscientists.
Ha: The spirituality categoryproportions are the same for natural scientists and socialscientists.
Calculate the test statistic. (Round your answer to two decimalplaces.)
?2 =
What is the P-value for the test? (Round your answer tofour decimal places.)
P-value =
What can you conclude?
Do not reject H0. There is not enoughevidence to conclude that the spirituality category proportions arenot all the same for natural scientists and social scientists.
Do not reject H0. There is not enoughevidence to conclude that there is an association between naturalscientists and social scientists.
Reject H0. There is convincing evidence toconclude that there is an association between natural scientistsand social scientists.
Reject H0. There is convincing evidence toconclude that the spirituality category proportions are not all thesame for natural scientists and social scientists.
