Question

. In a study to determine whether an association exists between maternal rubella and congenital cataracts, samples of 20 children with congenital cataracts and 25 children without congenital cataracts were selected. The mother of each child was asked whether she had rubella while carrying the child. The data are given below. Assume that all z-based methods are valid.

RUBELLA	CATARACTS
Frequency Row Pct	1_YES	2_NO	Total
1_YES	14 58.33	10 41.67	24
2_NO	6 28.57	15 71.43	21
Total	20	25	45

Statistic	DF	Value	Prob
Chi-Square	1	4.0179	0.0450
Likelihood Ratio Chi-Square	1	4.0979	0.0429
Continuity Adj. Chi-Square	1	2.9029	0.0884
Mantel-Haenszel Chi-Square	1	3.9286	0.0475
Phi Coefficient		0.2988
Contingency Coefficient		0.2863
Cramer's V		0.2988

Column 1 Risk Estimates
	Risk	ASE	95% Confidence Limits		Exact 95% Confidence Limits
Row 1	0.5833	0.1006	0.3861	0.7806	0.3664	0.7789
Row 2	0.2857	0.0986	0.0925	0.4789	0.1128	0.5218
Total	0.4444	0.0741	0.2993	0.5896	0.2964	0.6000
Difference	0.2976	0.1409	0.0215	0.5737
Difference is (Row 1 - Row 2)

Problem 6, cont.

a. What are the null and alternative hypotheses? Be sure to define any symbols that you use.

b. underline the following for testing that the proportion of children who have congenital cataracts differs significantly between mothers who had rubella and mothers who did not and fill in the blanks.

test statistic _______________          degrees of freedom _______________          p-value ________________

1.   Based on your answer in part b, what is the result of the test? Circle or underline your answer.

                                    Reject H₀                                Fail to Reject H₀

State your conclusion from the hypothesis test in the context of the applied problem.

c. underline the following for the difference in the proportion of children who have congenital cataracts between mothers who had rubella and mothers who did not and fill in the blanks:

Point estimate __________________           95% Confidence Interval ______________________   

d. Interpret your confidence interval in the context of the applied problem.

Answer 1

null hypotheses:

the proportion of children who have congenital cataracts significantlysame as between mothers who had rubella and mothers who did not

alternate hypothesis:

the proportion of children who have congenital cataracts differs significantly between mothers who had rubella and mothers who did not

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b)test statistic ______4.0179_________          degrees of freedom _______1________        

p-value ______0.0450__________

alpha=0.05

p value is less than alpha value, si,

reject Ho.

there is enough evidence to conclude that the proportion of children who have congenital cataracts differs significantly between mothers who had rubella and mothers who did not

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c)

Point estimate _______0.2976___________       

d)

one can be 95% confident that  difference in the population proportion of children who have congenital cataracts between mothers who had rubella and mothers who did not lies with the confidence interval