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 1.56 and the standard deviation was 0.11. 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?"

Answer 1

sample mean, xbar = 1.56
sample standard deviation, s = 0.11
sample size, n = 4
degrees of freedom, df = n - 1 = 3

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.35

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (1.56 - 2.35 * 0.11/sqrt(4) , 1.56 + 2.35 * 0.11/sqrt(4))
CI = (1.431 , 1.689)

Therefore, based on the data provided, the 90% confidence interval for the population mean is 1.431 < μ < 1.689 which indicates that we are 90% confident that the true population mean μ is contained by the interval (1.431 , 1.689)