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. The results are as follows: Find a 95% confidence interval for the difference between the mean numbers of fragments.

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Answer 1

Textbook Question

Chapter 5, Problem 1SE

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. The results are as follows:

Chapter 5, Problem 1SE, A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain

Find a 95% confidence interval for the difference between the mean numbers of fragments.

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 + ...

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

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Answer 2

Textbook Question

Chapter 5, Problem 1SE

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. The results are as follows:

Chapter 5, Problem 1SE, A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain

Find a 95% confidence interval for the difference between the mean numbers of fragments.

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 + ...

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Textbook Question

Chapter 5, Problem 1SE

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. The results are as follows:

Chapter 5, Problem 1SE, A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain

Find a 95% confidence interval for the difference between the mean numbers of fragments.

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 + ...

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Textbook Question

Chapter 5, Problem 1SE

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. The results are as follows:

Chapter 5, Problem 1SE, A molecular biologist is studying the effectiveness of a particular enzyme to digest a certain

Find a 95% confidence interval for the difference between the mean numbers of fragments.

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 + ...

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Answer 8

Expert Solution & Answer

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software:

Choose Stat > Basic Statistics > Paired t.
In First Sample, enter the column of Enzyme absent.
In Second Sample, enter the column of Enzyme present.
Check Options; enter Confidence level as 95%.
Choose not equal in alternative.
Click OK.

Output using the MINITAB software is given below:

Statistics for Engineers and Scientists, Chapter 5, Problem 1SE

From the output, the 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

To determine

Find the 95% confidence interval for the difference between the mean number of fragments.

Answer 12

Answer to Problem 1SE

The 95% confidence interval for the difference between the mean number of fragments is (1.943,19.724)_.

Answer 13

Explanation of Solution

Given info:

In the study, six DNA samples into two parts, treats one part with the enzyme and leaves the other part untreated. Also, count the number of DNA fragments that contain the given sequence.

Calculation:

Confidence interval:

Software Procedure:

Step-by-step procedure to obtain the confidence interval using the MINITAB software: