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 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  4322=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...