Refer to Exercise 1. Another molecular biologist repeats

Problem 2SE Chapter 5

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition

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Problem 2SE

Refer to Exercise 1. 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	24

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 repeats the study with a different design.

Then a molecular biologist makes up 12 DNA samples and 6 treated with the enzyme.

We know that 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	12	23
2	15	39
3	14	37
4	22	18
5	22	26
6	20	24

From the given information we know that ${n}_{1}=6$ and ${n}_{2}=6$ .

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

${(\overline{x}}_{1}-{\overline{x}}_{2})\pm{}t\left({\frac{{\left({\frac{{s}_{1}^{2}}{{n}_{1}}+\frac{{s}_{2}^{2}}{{n}_{2}}}\right)}^{2}}{\frac{{\left({\frac{{s}_{1}^{2}}{{n}_{1}}}\right)}^{2}}{{n}_{1}-1}+\frac{{\left({\frac{{s}_{2}^{2}}{{n}_{2}}}\right)}^{2}}{{n}_{2}-1}}}\right)$

Then the table is given below.

	Enzyme absent	Enzyme present
1	23	12
2	39	15
3	37	14
4	18	22
5	26	22
6	24	20

Now we are finding ${\overline{x}}_{1}$ , ${\overline{x}}_{2}$ , ${s}_{1}$ and ${s}_{2}$ .

The formula of the ${\overline{x}}_{1}$ is

${\overline{x}}_{1}=\frac{\Sigma{}{x}_{i}}{{n}_{1}}$

${\overline{x}}_{1}=\frac{105}{6}$

${\overline{x}}_{1}=17.5$

Therefore the formula of the ${\overline{x}}_{1}$ is 17.5.

Then the formula of the ${\overline{x}}_{2}$ is

${\overline{x}}_{2}=\frac{\Sigma{}{x}_{i}}{{n}_{2}}$

${\overline{x}}_{2}=\frac{167}{6}$

${\overline{x}}_{2}=27.8333$

Therefore the formula of the ${\overline{x}}_{2}$ is 27.8333.

The formula of the standard deviation is

${s}_{1}$ = $\sqrt{\frac{{\left({\Sigma{}{x}_{i}-{\overline{x}}_{1}}\right)}^{2}}{{n}_{1}-1}\ \ }$

${s}_{1}$ = $\sqrt{\frac{95.5}{6-1}\ \ }$

${s}_{1}$ = $\sqrt{\frac{95.5}{5}\ \ }$

${s}_{1}$ = $\sqrt{19.1}$

${s}_{1}$ = 4.3703

Therefore the standard deviation...

Step 2 of 3

Chapter 5, Problem 2SE is Solved

Step 3 of 3

Textbook: Statistics for Engineers and Scientists

Edition: 4th

Author: William Navidi

ISBN: 9780073401331

Since the solution to 2SE from 5 chapter was answered, more than 243 students have viewed the full step-by-step answer. Statistics for Engineers and Scientists was written by and is associated to the ISBN: 9780073401331. The answer to “Refer to Exercise 1. 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:12151422 22 20 Enzyme absent: 23 39 371826 24Find a 95% confidence interval for the difference between the mean numbers of fragments.” is broken down into a number of easy to follow steps, and 64 words. This full solution covers the following key subjects: another, biologist, chooses, confidence, Design. This expansive textbook survival guide covers 153 chapters, and 2440 solutions. The full step-by-step solution to problem: 2SE from chapter: 5 was answered by , our top Statistics solution expert on 06/28/17, 11:15AM. This textbook survival guide was created for the textbook: Statistics for Engineers and Scientists , edition: 4th.