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# A molecular biologist is studying the effectiveness of a ISBN: 9780073401331 38

## Solution for problem 1SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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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:

 Sample 1 2 3 4 5 6 Enzymepresent 22 16 11 14 12 30 Enzyme absent 43 34 16 27 10 40

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

Step-by-Step Solution:

Step 1 of 1:

Given a molecular biologist divides 6 DNA sample into two parts.

First one is enzyme present and  enzyme absent.

Then the data is given below.

 sample Enzyme present Enzyme absent 1 22 43 2 16 34 3 11 16 4 14 27 5 12 10 6 30 40

From the given information we know that and .

Our goal is:

We need to  find the 95% confidence interval for the difference between the mean number of fragments.

Now we have to find the 95% confidence interval for the difference between the mean number of fragments.

The formula of the confidence interval for the difference between the means is Here we subtracted enzyme absent and enzyme present.

Then the table is given below.

 Enzyme present Enzyme absent Difference 1 22 43 43-22=21 2 16 34 18 3 11 16 5 4 14 27 13 5 12 10 -2 6 30 40 10

Now we are finding ,and .

The formula of the is   Therefore, is...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073401331

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