Question Completion Status: QUESTION TO A randomized controlled trial is run to

Question

Question Completion Status: QUESTION TO A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to either the new drug or placebo (125 per group). There are 63 boys assigned to the new drug group and 58 boys assigned to the placebo. Is there a statistically significant difference in the proportions of boys assigned to the treatments? Apply the appropriate test at a 5% level of significance. (2 points) (2 points) 1. Critical value-+/- 2. Computed statistics 3. Based on comparing the computed statistic to the critical value which of the following is (are) true? (6 points) ere is significant evidence. alnha-0.05. that there is a difference in the

Explanation / Answer

Hypothesis:
Null hypothesis: p1 = p2
alternative Hypothesis: p1 not equal to p2

1)
Critical value for 5% = +/- 1.96

2)
p1 = 63/125 = 0.504 , n1 = 125
p2 = 58/125 = 0.464 , n2 = 125

The overall sample proportion is:
p = 63 + 58 / 250 = 0.484

z = (p1 - p2) / sqrt(p * (1 -p) *(1/n1 + 1/n2)
= ( 0.504 - 0.464)/ sqrt ( 0.484 * ( 1 - 0.484) * ( 1/125 + 1/125))
= 0.6328

3)
As calculated value of test statitstics is less than 1.96

There is not significant evidence, alpha = 0.05, that there is a difference in proportions of boys assigned to the treatments. (option b)

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