Scientists are working on a synthetic vaccine (antigen) for a particular parasit

Question

Scientists are working on a synthetic vaccine (antigen) for a particular parasite. The success of the vaccine hinges on the characteristics of DNA in peptide (protein) produced by the antigen. In one study, scientists tested alleles of antigen-produced protein for level of peptide. For a sample of 4 alleles, the mean peptide score was 1.54 and the standard deviation was 0.170 a. Use this information to construct a 90% confidence interval for the true mean peptide score in alleles of the antigen-produced protein. b. Interpret the interval for the scientists. c. What is meant by the phrase "90% confidence?"

Explanation / Answer

a.
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=1.54
Standard deviation( sd )=0.17
Sample Size(n)=4
Confidence Interval = [ 1.54 ± t a/2 ( 0.17/ Sqrt ( 4) ) ]
= [ 1.54 - 2.353 * (0.085) , 1.54 + 2.353 * (0.085) ]
= [ 1.34,1.74 ]
b.
Interpretations:
1) We are 90% sure that the interval [1.34 , 1.74 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population mean  
c.
it represents how confident we are at the given level of significance

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

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