Researchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adults diagnosed with acute sinusitis to one of two groups: treatment or control. Study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. The placebo consisted of symptoatic treatments such as acetaminophen, nasal decongestants, etc. At the end of the 10-day period, patients were asked if they experienced improvement in symptoms. The distribution of responses is summized below.  We want to test if there is a difference in the improvement rates of sinusitis symptoms between the treatment and the placebo. (a) Formulate the null and alternative hypotheses (b) Calculate the test statistic and find the P-value (c) Please check the conditions required to do the test above.

Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter11: Data Analysis And Displays
Section11.5: Choosing A Data Display
Problem 19E
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Researchers studying the effect of antibiotic treatment for acute sinusitis compared to symptomatic treatments randomly assigned 166 adults diagnosed with acute sinusitis to one of two groups: treatment or control. Study participants received either a 10-day course of amoxicillin (an antibiotic) or a placebo similar in appearance and taste. The placebo consisted of symptoatic treatments such as acetaminophen, nasal decongestants, etc. At the end of the 10-day period, patients were asked if they experienced improvement in symptoms. The distribution of responses is summized below. 

We want to test if there is a difference in the improvement rates of sinusitis symptoms between the treatment and the placebo.
(a) Formulate the null and alternative hypotheses
(b) Calculate the test statistic and find the P-value
(c) Please check the conditions required to do the test above.

Self-reported improvement
in symptoms
Yes
No
Total
Treatment
66
19
85
Group
Control
65
16
81
Total
131
35
166
Transcribed Image Text:Self-reported improvement in symptoms Yes No Total Treatment 66 19 85 Group Control 65 16 81 Total 131 35 166
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9781680331141
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HOUGHTON MIFFLIN HARCOURT
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Houghton Mifflin Harcourt