Question

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.

Answer 1

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)