Question

Use the following information to answer the questions below:

Research published in the journal Cough in 2012 examined the records of 241 children who visited a pediatrician with a severe cough. They found that coughing stopped in 47% of the 101 children who were treated with the non-opiate cough suppressant levodropropizine compared with 28% of the 60 children treated with cough suppressants containing opiates and 20% of the 80 children who were not prescribed anything for their coughs. The difference in cough relief was found to be statistically significant. However, in reviewing the study a critic pointed out that pediatricians are known to be hesitant to prescribe opiate based cough suppressants in very young children except in very specific medical circumstances.

If the sample size in this study involved only 80 children instead of 241, but the percentage of children who’s cough stopped was the same in all groups, then

Group of answer choices

the p-value would be smaller and results would definitely still be statistically significant.

the p-value would be bigger and the results may or may not still be significant.

the p-value would be smaller and the results may or may not still be significant.

the p-value would be bigger and the results would definitely still be significant.

Answer 1

Here, we see that the sample size is reduced from 241 to 80, but the percentage of children who's cough stopped was the same in all groups. We know that, when we reduce the sample size, the p-value becomes higher and the chance of rejection of the null hypothesis becomes lesser. Here, the result is statistically significant for 241 children , so, if we reduce the sample size, the p-value would become higher and the results may or not be still statistically significant. The correct answer is:

the p-value would be bigger and the results may or may not still be significant.