## Question

###### 4. Rours et al. (2005) collected urine specimens from 750 asymptomatic pregnant women in Rotterdam, Netherlands,...

4. Rours et al. (2005) collected urine specimens from 750 asymptomatic pregnant women in Rotterdam, Netherlands, to estimate the prevalence of chlamydia among the corre- sponding population. Of the 750 specimens, 48 tested positive for the disease. Using this information, answer the following: (a) Describe the assumptions that would be needed in order to use one binomial distribution for the sample. (b) Presuming the assumptions in part (a) are satisfied, find a confidence interval to estimate the prevalence of chlamydia. Use the most appropriate confidence interval procedure for this problem, and interpret the results.

## Answers

Here we have

n=750, x = 48

(a)

Specimens should be independent. Probability of getting positive result should be constant from trial to trial.

(b)

Since number of successes 48 and number of failures 750 -48 = 702 are greater than 5 so normal approximation can be used. The 95% confidence interval is:

Here we have x =48, n = 750, p = x =0.064 Level of significance: -0.05 Critical value: Z 1.96 The standard deviation is: p(1-p) 20-2) =sqrt((0.064*(1-0.064))/750) 0.0089 The requried confidence interval is: c.Ơp (1.96*0.0089) -0.064 -0.064 0.0174 (0.047,0.081) p Excel function for critical value: NORMSINV(1-(0.05/2)) Hence, the required confidence interval is (0.047,0.081)

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