A research study was conducted to test a new antibiotic for conjunctivitis. The

Question

A research study was conducted to test a new antibiotic for conjunctivitis. The efficacy of the antibiotic was compared in adults with prior symptoms of conjunctivitis. After the antibiotic or a placebo was given to the patients, the status of the conjunctivitis was evaluated and recorded at 5, 10 and 15 days by a physician. In table 1, it is reported the number of patients with conjunctivitis after 5 days for three groups: a) treated; b) placebo; c) untreated.

Table 1. Number of patients with conjunctivitis after 5 days of treatment.

a) Estimate the prevalence of conjunctivitis in the untreated group after 5 days. Provide a 95% confidence interval for the prevalence.

b) Determine a 95% confidence interval for the prevalence of conjunctivitis in the treated group after 5 days of treatment.

c) Determine whether the prevalence of conjunctivitis for the treated group differs from that of the untreated group using a contingency table approach. Provide p-value for two-tailed ( = 0.01).

d) Are the absence of conjunctivitis and treatment dependent or independent events?

Group Number of Adults Number of Adults with Conjunctivitis Treated 102 3 Placebo 154 70 Untreated 160 85

Explanation / Answer

Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=85
Sample Size(n)=160
Sample proportion = x/n =0.531
Confidence Interval = [ 0.531 ±Z a/2 ( Sqrt ( 0.531*0.469) /160)]
= [ 0.531 - 1.96* Sqrt(0.002) , 0.531 + 1.96* Sqrt(0.002) ]
= [ 0.454,0.608]

B.
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=3
Sample Size(n)=102
Sample proportion = x/n =0.029
Confidence Interval = [ 0.029 ±Z a/2 ( Sqrt ( 0.029*0.971) /102)]
= [ 0.029 - 1.96* Sqrt(0) , 0.029 + 1.96* Sqrt(0) ]
= [ -0.004,0.062]

Note: As - per chegg, experts - only - solve - one- question -per -thread. Please -ask -the -remaining -in -different- post

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.