Question

samples of dna are collected, and the four dna bases of a, g, c, and t are coded as 1, 2, 3, and 4, respectively. the results are listed below. construct a 90% confidence interval estimate of the mean. what is the practical use of the confidence interval?
1, 1, 2, 3, 4, 3, 4, 3, 3, 2
what is the confidence interval for the population mean μ?
2.0 < μ < 3.2 (round to one decimal place as needed.)
what is the practical use of the confidence interval? select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a. the confidence interval can be used to estimate that 90% of all people have dna bases between □ and □.
(round to one decimal place as needed.)
b. the confidence interval can be used to estimate that, with 90% confidence, the interval from □ to □ actually contains the true mean dna base of all people.
(round to one decimal place as needed.)
c. the given numbers are just substitutes for the four dna base names, so the numbers do not measure or count anything, and they are at the nominal level of measurement. the confidence interval has no practical use.

Explanation:

A confidence interval for the population mean gives a range of values within which we can be confident (in this case, 90% confident) that the true population mean lies. Option A is incorrect because a confidence interval for the mean is not about estimating the proportion of individuals (90% of all people having DNA bases in an interval). Option C is incorrect as the numbers, while substitutes, can still be used in statistical analysis for the mean. Option B correctly states the purpose of a confidence interval for the mean - estimating with a certain level of confidence (90% here) that the interval contains the true population mean.

Answer:

B. The confidence interval can be used to estimate that, with 90% confidence, the interval from \(2.0\) to \(3.2\) actually contains the true mean DNA base of all people.