# statistics

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1. Prospective Cohort Study
The following tables show the crude and sex-specific results from a Prospective Cohort Study that examines the association between a binary exposure (E) and the development of a disease (D) during 20 years of follow-up.
Full Data:

Sex-Specific Data:
Males

Females

1. Assume that this cohort is a simple random sample from a broader population of interest. Model the number of disease positive individuals among all exposed individuals in the sample using the binomial distribution with probability of disease ; and model the number of disease positive individuals among the unexposed in the sample using a binomial distribution, with probability of disease . Estimate , the proportion of exposed individuals who are disease positive, and provide an exact 95% confidence interval.
Estimated Proportion:

Confidence Interval:
Lower Bound:

Upper Bound:

2. Would you expect the large-sample Wilson confidence interval to provide similar results to the exact confidence intervals in question 1?
Yes No

3. Consider the following hypothetical scenario. Suppose that the data generating mechanism was different, and the data were generated from a stratified random sample of the population, where the probability of disease varies by stratum and the sampling probabilities vary by stratum. For instance, suppose the sampling was stratified by gender, where males were oversampled. Would the binomial model described in question 1 still be appropriate for estimating the proportion of diseased positive individuals in the population within exposure groups? (Model the number of disease positive individuals among all exposed individuals in the sample using the binomial distribution; and model the number of disease positive individuals among the unexposed in the sample using a binomial distribution).
Yes No

4. Now, we examine the risk difference between the exposed and unexposed populations. Estimate the risk difference for the disease and construct a corresponding large-sample 95% confidence interval. Calculate the risk difference as the proportion of diseased individuals in the exposed minus the proportion of diseased individuals in the unexposed.
Risk Difference:

Confidence Interval:
Lower Bound:

Upper Bound:

5. Conduct a two-sample proportion test that the risk difference is equal to zero (versus the alternative that the risk difference is not equal to zero) at the 0.05 level of significance.
What is the absolute value of the test statistic?

What is the distribution of the test statistic under the null hypothesis?
Standard Normal t-distribution Binomial

What is the p-value?

(A) We have evidence that the risk difference is not equal to 0.
(B) We do not have evidence that the risk difference is different from zero.
(C) None of the above.

6. Rather than testing that the risk difference is equal to 0 (as in question 5), could you have conducted a Pearson-chi square test to test for an association between disease and exposure?
Yes No

7. What is the value for the Crude Risk Ratio, comparing exposed subjects to non-exposed subjects?

8. Using the Mantel-Haenszel formula, what is the value for the sex-adjusted Risk Ratio, comparing exposed subjects to non exposed subjects?

9. Using the total data as a standard population, what is the value for the Standardized Risk Ratio?

10. Is sex a confounder in this study? (enter the letter of your best answer from the options listed below)
(A) Yes, because the crude RR equals the sex-adjusted RR
(B) No, because the crude RR equals the sex-adjusted RR
(C) Yes, because the crude RR does not equal the sex-adjusted RR
(D) No, because the crude RR does not equal the sex-adjusted RR
(E) Yes, because the RR among the males equals the RR among the females
(F) No, because the RR among the males equals the RR among the females

11. Using the Risk Ratio as a measure of association, is sex an effect modifier in this study?
Yes, because the crude RR equals the sex-adjusted RR No, because the crude RR equals the sex-adjusted RR Yes, because the crude RR does not equal the sex-adjusted RR No, because the crude RR does not equal the sex-adjusted RR Yes, because the RR among males equals the RR among females No, because the RR among males equals the RR among females

• statistics -

We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.

Also your data will not come through via copy and paste.

• statistics -

could u please at least suggest the steps to do it

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