HINT GIVEN: How can we compute the confidence interval for the difference between two means? A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain sequence of DNA nucleotides. He dividessix DNA samples into two parts, treats one part with the enzyme, and leaves the other part untreated. He then uses a polymerasechain reaction assay to count the number of DNA fragments that contain the given sequence. Another molecular biologist repeats thestudy with a different design. She makes up 12 DNA samples, and then chooses 6 at random to be treated with the enzyme and 6 toremain untreated. The results are as follows:Enzyme present: 12 15 14 22 22 20Enzyme absent: 23 39 37 18 26 23Let μx represent the population mean with the enzyme absent and let μy represent the population mean with the enzyme present.Find a 95% confidence interval for the difference μx - My (Round the final answers to three decimal places.)The 95% confidence interval is ( 1.63418.699 >).

The objective of this question is to calculate the 95% confidence interval for the difference…

Answered: A molecular biologist is studying the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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HINT GIVEN: How can we compute the confidence interval for the difference between two means?

A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain sequence of DNA nucleotides. He divides
six DNA samples into two parts, treats one part with the enzyme, and leaves the other part untreated. He then uses a polymerase
chain reaction assay to count the number of DNA fragments that contain the given sequence. Another molecular biologist repeats the
study with a different design. She makes up 12 DNA samples, and then chooses 6 at random to be treated with the enzyme and 6 to
remain untreated. The results are as follows:
Enzyme present: 12 15 14 22 22 20
Enzyme absent: 23 39 37 18 26 23
Let μx represent the population mean with the enzyme absent and let μy represent the population mean with the enzyme present.
Find a 95% confidence interval for the difference μx - My (Round the final answers to three decimal places.)
The 95% confidence interval is ( 1.634
18.699 >).

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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