Researchers studying the effect of antibiotic treatment compared to symptomatic treatment for acute sinusitis randomly assigned 166 adults diagnosed with sinusitis into two groups. Participants in the antibiotic group received a 10-day course of an antibiotic, and the rest received symptomatic treatments as a placebo. These pills had the same taste and packaging as the antibiotic. At the end of the 10-day period patients were asked if they experienced improvement in symptoms since the beginning of the study. The distribution of responses is summarized below.
|
Antibiotic
|
Placebo
|
Total
|
Yes
|
72
|
60
|
132
|
No
|
13
|
21
|
31
|
Total
|
85
|
81
|
166
|
A simulation was conducted under the assumpton that the proportion of self-reported improvement with the antibiotic treatment is equal to the proportion of self-reported improvement with the palcebo. 100,000 simulated differences were generated to construct the null distribution shown. The value ˆpa,∼p^a,∼ represents the proportion of self-reported improvement with antibiotic treatment, and ˆpp,∼p^p,∼ is the proportion of self-reported improvement with the placebo treatment.
b) Calculate the observed difference between the proportion of self-reported improvement with antibiotic and proportion of self-reported improvement with placebo.
Round to the nearest ten-thousandth: ˆpa−ˆppp^a-p^p=
c) Estimate the p-value using the figure above.
d) Determine the conclusion of the hypothesis test.
- We should not reject the null hypothesis.
- We should reject the null hypothesis.
Extracted text: A simulation was conducted under the assumpton that the proportion of self-reported improvement with the antibiotic treatment is equal to the proportion of self-reported improvement with the palcebo. 100,000 simulated differences were generated to construct the null distribution shown. The value p, the proportion of self-reported improvement with antibiotic treatment, and p, is the proportion of self- represents reported improvement with the placebo treatment. Simulaion of Antibiotic vs. Placebo Response, trails = 100,000, n1 = 85, n2 = 81 %3D -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 p_hat_a - p_hat_p a) Suppose the researchers want to determine, at a 5% significance level, if there is a difference in proportion of self-reported improvement with antibiotics and proportion of self-reported improvement with placebo. What are the hypotheses? Но: Ра — Р. [?0 На: Ра — Р. ?0 b) Calculate the observed difference between the proportion of self-reported improvement with antibiotic and proportion of self-reported improvement with placebo. Round to the nearest ten-thousandth: Pa – Pn c) Estimate the p-value using the figure above. d) Determine the conclusion of the hypothesis test. O We should not reject the null hypothesis. relative frequency 0.10 0.20 0.30 00'0