Question

4. The drug Prevnar is a vaccine meant to prevent meningitis. It is typically administered to infants. In clinical trials, the vaccine was administered to 710 randomly sampled infants between 12 and 15 months of age. Of the 710 infants, 121 experienced a loss of appetite. Is this significant evidence to conclude that the proportion of infants who receive Prevnar and experience a loss of appetite is different than 0.135 which is the proportion of children who experience a loss of appetite with competing medications? Use an α of 0.05.
(a) State the null and alternative hypotheses.
(b) Calculate the test statistic.
(c) Report the p-value.
(d) State a conclusion in context of the problem.
(e) Calculate a 95% confidence interval for the proportion of infants on Prevnar who experience a loss of appetite. Interpret the confidence interval in context of the problem.
(f) Does your confidence interval agree with the results of the hypothesis test? Explain.

Answer 1

f. The confidence interval completely agrees with the result obtained in hypothesis testing. In hypothesis testing we get that the population proportion is different from 0.135 . And when we calculated 95% confidence interval of population proportion here we can also see that the interval doesn't contain the point 0.135 . Which implies that p can't be equal to 0.135. and this was our result in hypothesis testing also.