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 = 69 / 339 = 0.204

95% confidence interval for p is

- Z * sqrt ( ( 1 - ) / n) < p < + Z * sqrt ( ( 1 - ) / n)

0.204 - 1.96 * sqrt( 0.204 * 0.796 / 339) < p < 0.204 + 1.96 * sqrt( 0.204 * 0.796 / 339)

0.161 < p < 0.247

95% CI is ( 0.161 , 0.247 )

b)

Since all data values in confidence interval are greater than 0.1, we have sufficient evidence to

support the claim.