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.
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 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
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 ,,and .
The formula of the is
Therefore the formula of the is 17.5.
Then the formula of the is
Therefore the formula of the is 27.8333.
The formula of the standard deviation is
=
=
=
=
= 4.3703
Therefore the standard deviation is 4.3703.
Then the formula of the standard deviation is
=
=
=
=
= 8.3286
Therefore the standard deviation is 8.3286.
The 95% difference between mean is
The 95% of confidence interval is .
From the table value
The formula of the confidence interval for the difference between the means is
=
=
=
=
=
Therefore, the confidence interval is and .