Question

In the last 10 years, the prevalence of peanut allergies has doubled in Western countries. Is consumption or avoidance of peanuts in infants related to the development of peanut allergies in infants at risk? Subjects included infants between 44 and 11 months with severe eczema, an egg allergy, or both, but who did not display a preexisting sensitivity to peanuts based on a skin‑prick test. The infants were randomly assigned to either a treatment that avoided consuming peanut protein or a treatment in which at least 6 grams of peanut protein were consumed per week. The response was the presence or absence of a peanut allergy at 60 months of age. In the avoidance group containing 263 infants, 36 had developed a peanut allergy at 60 months of age, while in the consumption group containing 266 infants, 5 had developed a peanut allergy.

(a) Despite the large sample sizes in both treatments, why should we not use the large‑sample confidence interval for these data?

We should not use the large‑sample confidence interval for these data because the sample sizes are different.

We should not use the large‑sample confidence interval for these data because only 5 infants developed a peanut allergy in the consumption group.

None of the selections are correct.

We should not use the large‑sample confidence interval for these data because there are not enough samples for the consumption group.

(b) The plus four method adds one success and one failure to each sample. What are the sample sizes and counts of successes after you do this? Let ?A denote those who develop a peanut allergy after avoiding peanuts C those who develop a peanut allergy after consuming peanuts. (Enter your answers as whole numbers.)

??=

Count of successes in group ?=

??=

Count of successes in group ?=

(c) Give the plus four 99% confidence interval for the difference in the probabilities of developing a peanut allergy for the avoidance and consumption treatments (??−??). (Enter your answers as percentages rounded to two decimal places.)

Lower bound =____%

Higher bound =____%

What does your interval say about the comparison of these treatments in the context of the problem?

There is no conclusive evidence to say either will heighten the chance of developing a peanut allergy.

Infants with severe eczema are less likely to develop a peanut allergy by 60 months after avoiding peanuts compared to those who consume them, and those with an egg allergy are more likely to develop a peanut allergy by 60 months after avoiding peanuts compared to those who consume them.

Infants with severe eczema, an egg allergy, or both are more likely to develop a peanut allergy by 60 months after avoiding peanuts compared to those who consume them.

Infants with severe eczema, an egg allergy, or both are less likely to develop a peanut allergy by 60 months after avoiding peanuts compared to those who consume them.

Answer 1

(a)

We should not use the large‑sample confidence interval for these data because only 5 infants developed a peanut allergy in the consumption group.

(b)

??= 263+2 = 265

Count of successes in group ?= 36+1 = 37

??= 266+2 = 268

Count of successes in group ?= 5+1 = 6

(c)

Lower bound: 0.06

Upper bound: 0.18

Since confidence interval does not contain zero and all values are positive so correct option is

Infants with severe eczema, an egg allergy, or both are more likely to develop a peanut allergy by 60 months after avoiding peanuts compared to those who consume them.