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 44 ​alleles, the mean peptide score was 1.371.37 and the standard deviation was 0.110.11.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

Answer: a) (1.34, 1.40),

b) The interval above simply implies that the least value of mean peptide score in alleles is 1.34 and the highest value is 1.40,

c) it simply implies that we are 90% sure that the interval we has the population mean.

Step-by-step explanation: The question is requiring us to construct a 90% confidence interval for mean peptide score in alleles.

From the question, we have our parameters as follows.

Sample size (n) = 44

Sample mean (x) = 1.37

Sample standard deviation (s) = 0.11

The formulae for Constructing a 90% confidence interval for population mean is given below as

u = x + Zα/2 × s/√n.... For upper tailed

u = x - Zα/2 × s/√n.... For lower tailed

Zα/2 is the critical value for a 2 tailed test.

We are using a z score for our critical value {even though we are given sample standard deviation because our sample size is greater than 30 (n=44)}.

The value for Zα/2 is gotten from a standard normal distribution table and it value here is 1.64

By substituting the parameters, we have that

For lower limit

u = 1.37 - 1.64 × 0.11/√44

u = 1.37 - 1.64 (0.0166)

u = 1.37 - 0.0272

u = 1.34

For upper limit

u = 1.37 + 1.64 × 0.11/√44

u = 1.37 + 1.64 (0.0166)

u = 1.37 + 0.0272

u = 1.40.

Hence the 90% confidence interval for mean value of peptide score in alleles is (1.34, 1.40)

b)

The interval above simply implies that the least value of mean peptide score in alleles is 1.34 and the highest value is 1.40.

c) it simply implies that we are 90% sure that the interval we has the population mean.