Question

A clinical trial is conducted to compare an experimental
medication to placebo to reduce the symptoms of asthma. Two hundred
participants are enrolled in the study and randomized to receive
either the experimental medication or placebo. The primary outcome
is self-reported reduction of symptoms. Among 100 participants who
receive the experimental medication, 38 report a reduction of
symptoms as compared to 21 participants of 100 assigned to placebo.
When you test if there is a significant difference in the
proportions of participants reporting a reduction of symptoms
between the experimental and placebo groups. Use α = 0.05. What
should the researcher’s conclusion be for a 5% significance level?
Reject H_{0}

because 2.64 ≥ 1.960. We have statistically significant evidence at
α = 0.05 to show that there is a difference in the proportions of
patients reporting a reduction in symptoms.

We reject H |
||

We fail to reject H |
||

We fail to reject H |
||

We fail to reject H |

Answer #1

Let p1 be the proportion of participants who receive the experimental medication and reported a reduction of symptoms.

Given = 38/100 = 0.38

= 21/100 = 0.21

We need to check if there is significant difference in the proportions.

This corresponds to a two-sided test, for which a z-test for two population proportions needs to be conducted.

So accordingly the null and the alternate hypothesis would be:

pooled proportion = (38+21)/200 = 59/200 = 0.295

Standard error (SE) = = 0.064

Z-statistic would be = (0.38-0.21)/0.064 = 2.64

And for a significance level of 0.05, critical value of z = 1.96.

=> Reject Ho if z-statistic > 1.96

And z-statistiic = 2.64 > 1.96 , Hence reject Ho.

=> We have strong evidence against the null hypothesis and claim that the proportions are not equal.

=> Option 1 is correct.

A clinical trial is conducted to compare an experimental
medication to placebo to reduce the symptoms of asthma. Two hundred
participants are enrolled in the study and randomized to receive
either the experimental medication or placebo. The primary outcome
is self-reported reduction of symptoms. Among 100 participants who
receive the experimental medication, 38 report a reduction of
symptoms as compared to 21 participants of 100 assigned to placebo.
When you test if there is a significant difference in the
proportions...

A clinical trial is conducted to compare an experimental
medication to placebo to reduce the symptoms of asthma. Two hundred
participants are enrolled in the study and randomized to receive
either the experimental medication or placebo. The primary outcome
is self-reported reduction of symptoms. Among 100 participants who
receive the experimental medication, 38 report a reduction of
symptoms as compared to 21 participants of 100 assigned to placebo.
When you test if there is a significant difference in the
proportions...

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participants are enrolled in the study and randomized to receive
either the experimental medication or placebo. The primary outcome
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receive the experimental medication, 38 report a reduction of
symptoms as compared to 21 participants of 100 assigned to placebo.
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