Question

1. Comment about the change in proportion of atheists over the period.What are the conditions required to make the inferences in part (a) valid? Are the conditions met in this case? Explain briefly.

a) One sample proportion confidence interval:

Outcomes in : response

Success : atheist

Group by: year

p : Proportion of Successes

95% confidence interval results:

year	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
2005	1428	13608	0.10493827	0.0026272191	0.099789017	0.11008753
2012	3476	51927	0.066940127	0.0010967343	0.064790568	0.069089687

2. a. Is there convincing evidence that Canada has seen a change in the proportion of atheists between 2005 and 2012? significance level of 0.05 or 5% is shown below in table. In particular, state the null and alternative hypotheses, report the value of the test statistic, its distribution under the null hypothesis, and the p-value of the test. State your conclusions. explain the table briefly?

One sample proportion confidence interval:

Outcomes in : response of atheist where nationality= “Canada”

Success : atheist

Group by: year

p : Proportion of Successes

5% confidence interval results:

year	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
2005	1428	13608	0.10493827	0.0026272191	0.10477353	0.10510302
2012	3476	51927	0.066940127	0.0010967343	0.066871355	0.0670089

2.b a 95% confidence interval for the difference in the proportion of atheists in Canada between 2005 and 2012 is given below. explain the table.  Is the interval consistent with the conclusion reached in part (a)?

Two sample proportion confidence interval:

p1 : Proportion of successes (Success = atheist ) for response

p2 : Proportion of successes (Success = atheist) for response

p1 - p2 : Difference in proportions

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	0	65535	4904	65535	-0.074830243	0.0010278095	-0.076844713	-0.072815774

2.c Are the conditions for inference in parts (a) and (b) met in this case? Refer to the theory to answer the question?

3. the contingency table of response by income for the year 2012 is shown below. Comment briefly about the relationship between atheism rate and income level.

Contingency table results:

Rows: response
Columns: income

Cell format

Count
(Percent of total)

	high	lower-middle	upper-middle	Total
atheist	4084 (6.62%)	96 (0.16%)	597 (0.97%)	4777 (7.74%)
non-atheist	36668 (59.42%)	4949 (8.02%)	15312 (24.81%)	56929 (92.26%)
Total	40752 (66.04%)	5045 (8.18%)	15909 (25.78%)	61706 (100%)

Chi-Square test:

Statistic	DF	Value	P-value
Chi-square	2	891.84799	<0.0001

b. Using α = 0.01, test that there is no relationship between response and income. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion.

Answer 1