Question

Peanut allergy is increasingly common in Western countries. A study enrolled infants with a diagnosed peanut sensitivity and randomly assigned them to either avoid or regularly consume peanuts until 60 months of age. At the end of the study, 18 of the 51 children who had avoided peanuts were still allergic to peanuts. In contrast, 5 of the 47 children who had regularly consumed peanuts were still allergic to peanuts. We want to run a test to see if peanut allergy at 60 months is affected by the long-term consumption or avoidance of peanuts among children diagnosed in infancy with a peanut allergy.

(a) Check the conditions for inference and state the hypotheses. (b) Obtain the test statistic and p-value.

(c) Conclude in context.

Answer 1

a.)

-sample size is large enough i,e np >=5 and n(1-p) >=5 in both the cases.

b.)

c._)

as, significance level is not given, consider default significance(alpha=0.05)

Since, p-value<significance, reject the null hypothesis.

There are significant evidence to conclude that there is difference in the proportion of 60 months old affected by the long-term consumption or avoidance of peanuts among children diagnosed in infancy with a peanut allergy