Question

The drug Prevnar is meant to prevent certain types of bacterial meningitis. Subjects in Group 1 received Prevnar, while subjects in group 2 received a control vaccine. In some instances, subjects experienced fever as a side effect. In the table below, X designates that the subject experie sample from a population of interest. 9. nced fever as a side effect. Assume these observations can be treated as a random Sample 1. Prevnar 107.1710 2. Control Vaccine 67 611 [5 pts] Calculate a 95% confidence interval for the difference in the proportion of the experimental and control groups who experienced fever as a side effect. Interpret the confidence interval with a short sentence that includes the confidence level, a parameter, and the variable of interest, the lower bound and the upper bound a. Explain how to interpret the fact that 0 is not in the confidence interval. [5 pts] b.

Answer 1

Solution:-

9) a)

95% confidence interval for the difference in the proportions is C.I = ( 0.0049, 0.0772).

$C.I = \left (p_{1}-p_{2} \right )\pm z_{\alpha /2}\times \sqrt{\frac{p_{1}(1-p_{1})}{n_{1}}+\frac{p_{2}(1-p_{2})}{n_{2}}}$

C.I = (0.1507 - 0.1097) + 1.96 × 0.01844

C.I = 0.04104 + 0.03615

C.I = ( 0.0049, 0.0772)

b) Since the confidence interval does not contain 0, hence we can conclude that there is significant difference between two proportions.