# A group of researchers was concerned with the growing prevalence of peanut allergies in Western countries...

###### Question:

A group of researchers was concerned with the growing prevalence of peanut allergies in Western countries and decided to investigate the effectiveness of two alternative approaches to treatment. They recruited 98 infants with a diagnosed peanut allergy and randomly assigned them either to consume small amounts of peanuts regularly or to completely avoid peanuts until 60 months of age. At the end of that time they recorded which infants were still allergic to peanuts. The following plot and summary table were obtained from this data. Rows: Allergy Columns: Treatment Avoid Low Dose All Chart of Treatment Responses 40 Yes 18 35.29 5 23 10.64 23.47 30 No 33 64.71 42 75 89.36 76.53 Data 20 All 51 47 98 100.00 100.00 100.00 10 Cell Contents Count % of Column Allergy Yes No No Low Dose Avoid The researchers are interested in whether there is any statistical evidence that the proportions of infants with a peanut allergy in the general population who would still have allergies after treatment are different for the two treatment groups. They decide to carry out a relevant statistical test to determine this. Which of the following statements best represents the null hypothesis (Ho) for this test? Question 3 Which of the following statements is most appropriate with reference to the test described in Question 1? (a) Since the data used for this test is contained in a single binary variable, the most relevant test to perform is the exact binary test of one proportion. (b) Since the data being used for this test were all obtained from the same group of infants, the most relevant test to perform is McNemar's exact test for two related proportions. C) Since the numbers of infants in each group who do or don't still have an allergy after treatment are all at least 5, the most relevant test to perform is a two- proportion Z-test. (d) Since the data being used for this test relates to two different groups of infants, the most relevant test to perform is a Fisher exact test for two proportions.

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