Question

To evaluate the policy of routine vaccination of infants for whopping cough, adverse reactions were monitored in 339 infants who received their first injection of vaccine. Reactions were noted in 69 of the infants.

a. Construct a 95% confidence interval for the proportion of infants that suffered from adverse reactions.

b. Does the data provide significant evidence that the proportion of infants that suffered from adverse reactions was greater than 0.1? Use a significance level of 0.01.

Answer 1

a)
sample proportion, pcap = 0.2035
sample size, n = 339
Standard error, SE = sqrt(pcap * (1 - pcap)/n)

SE = sqrt(0.2035 * (1 - 0.2035)/339) = 0.0219

For 95% Confidence level, the z-value = 1.96

CI = (xbar - z*SE, xbar + z*SE)
CI = (0.2035 - 1.96 * 0.0219 , 0.2035 + 1.96 * 0.0219)

CI = (0.1606 , 0.2464)

b)
H0: p = 0.1
Ha: p > 0.1

Test statistic,
z = (0.2035 - 0.1)/sqrt(0.1 * 0.9/339)
z = 6.35

p-value = 0.000

As p-value < 0.01, reject H0
there are significant evidence to conclude that the proportion is greater than 0.1