In: Math
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 | 54 | 158 | 193 | 211 |
Social Scientists | 57 | 227 | 240 | 242 |
State the null and alternative hypotheses.
H0: The spirituality category proportions
are not all the same for natural scientists and social
scientists.
Ha: The spirituality category
proportions are the same for natural scientists and social
scientists. H0: The spirituality category
proportions are the same for natural scientists and social
scientists.
Ha: 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.
Ha: The spirituality category for
natural scientists and social scientists are not independent.
H0: The spirituality category for natural
scientists and social scientists are not independent.
Ha: The spirituality category for
natural scientists and social scientists are independent.
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. Reject H0. There is convincing evidence to conclude that there is an association between 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 the spirituality category proportions are not all the same for natural scientists and social scientists.
You may need to use the appropriate table in Appendix A to answer
this question.
H0: The spirituality category proportions
are the same for natural scientists and social scientists.
Ha: The spirituality category
proportions are not all the same for natural scientists and social
scientists.
Observed Frequencies | |||||||
column | |||||||
0 | Very | Moderate | Slightly | Not at All | Total | ||
Natural Scientists | 54 | 158 | 193 | 211 | 616 | ||
Social Scientists | 57 | 227 | 240 | 242 | 766 | ||
Total | 111 | 385 | 433 | 453 | 1382 | ||
Expected frequency of a cell = sum of row*sum of column / total sum | |||||||
Expected Frequencies | |||||||
Very | Moderate | Slightly | Not at All | Total | |||
Natural Scientists | 111*616/1382=49.476 | 385*616/1382=171.606 | 433*616/1382=193.001 | 453*616/1382=201.916 | 616 | ||
Social Scientists | 111*766/1382=61.524 | 385*766/1382=213.394 | 433*766/1382=239.999 | 453*766/1382=251.084 | 766 | ||
Total | 111 | 385 | 433 | 453 | 1382 | ||
(fo-fe)^2/fe | |||||||
Natural Scientists | 0.414 | 1.079 | 0.000 | 0.409 | |||
Social Scientists | 0.333 | 0.868 | 0.000 | 0.329 |
Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe = 3.43
Number of Rows = 2
Number of Columns = 4
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 4- 1 )
= 3
p-Value = 0.3300
Decision: p value > α , do not reject
Ho
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.