A large randomised trial of a synbiotic (mixture of probiotics and prebiotics) treatment for preventing sepsis in early infancy was carried out in a part of India with high infant mortality. The outcome was either sepsis or death in the first 60 days after birth.

There were exactly 2,278 infants randomised to each of the two groups (synbiotic or control). The numbers of cases of sepsis/death in the first 60 days were:

Control: 206

Synbiotic: 123

Find an estimate of the true difference in the proportion of children with sepsis/death in the first 60 days after birth in the two groups (Control minus Synbiotic). Report the result to three decimal places. Make sure your answer is a difference of proportions, not a difference of percentages.

Question

A large randomised trial of a synbiotic (mixture of probiotics and prebiotics) treatment for preventing sepsis in early infancy was carried out in a part of India with high infant mortality.   The outcome was either sepsis or death in the first 60 days after birth.

There were exactly 2,278 infants randomised to each of the two groups (synbiotic or control). The numbers of cases of sepsis/death in the first 60 days were:

Control: 206

Synbiotic: 123

Find an estimate of the true difference in the proportion of children with sepsis/death in the first 60 days after birth in the two groups (Control minus Synbiotic).  Report the result to three decimal places.  Make sure your answer is a difference of proportions, not a difference of percentages.

BlackTom AI · Accepted Answer

First, restating the data helps ensure we’re comparing the correct groups and outcomes. The trial had 2,278 infants in each group (control and synbiotic). The numbers of sepsis/death in the first 60 days were 206 in the control group and 123 in the synbiotic group. We are asked for the true difference in proportions, defined as Control minus Synbiotic, expressed as a proportion (not a percentage).

Step-by-step calculation:
- Compute the number of events reduced by the synbiotic: 206 − 123 = 83 fewer cases in the synbiotic group.
- Compute the proportion in each group by dividing by the group size: 
  - Control proportion = 206/2278
  - Synbiotic proportion = 123/2278
- The difference in proportions (Control − Synbiotic) is (206/2278) − (123/2278) = (206 − 123)/2278 = 83/2278.
- Evaluate 83/2278 as a decimal to three decimal places. Doing the division: 83 ÷ 2278 ≈ 0.036435... 
- Rounding to three decimal places gives 0.036.

Why this matches the requested format:
- We did not use a percentage; we kept the result as a proportion (a unitless fraction of the sample).
- The arithmetic relies only on the shared denominator 2278, so differences in the event counts translate directly into the proportion difference.

Common potential misunderstandings to avoid:
- Mixing up the order of subtraction: they specifically want Control minus Synbiotic, not the reverse.
- Converting to a percentage before rounding: the instruction asks for a difference of proportions, not a difference of percentages.
- Forgetting to divide by the correct group size: each proportion must be computed with its own group size (here both are the same, 2278), and the difference must reflect those proportions, not raw counts.

Contextual check:
- The result 0.036435... is a small, positive difference indicating fewer sepsis/death events in the synbiotic group relative to control, as expected if the synbiotic has a protective effect.
- Rounding to three decimals yields 0.036, which matches the required reporting precision.

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Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 ​ ​ Refer to Exhibit 10-10. The standard error of is _____.

Questions 8 and 9 continued: Report the upper limit of the confidence interval to three decimal places. Make sure your answer is a difference of proportions, not a difference of percentages.

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Exhibit 10-10 The results of a recent poll on the preference of shoppers regarding two products are shown below. Product Shoppers Surveyed Shoppers Favoring This Product A 800 560 B 900 612 Refer to Exhibit 10-10. The standard error of is _____.

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