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#1 2013-03-22 01:51:50

ShivamS
Super Member

Online

Stats

Twenty-two students were randomly selected from a population of 1000 students. The sampling method was simple random sampling. All of the students were given a standardized English test and a standardized math test. Test results are summarized below.

Student    English    Math    Difference, d    (d - d)2
1    95    90    5    16
2    89    85    4    9
3    76    73    3    4
4    92    90    2    1
5    91    90    1    0
6    53    53    0    1
7    67    68    -1    4
8    88    90    -2    9
9    75    78    -3    16
10    85    89    -4    25
11    90    95    -5    36
Student    English    Math    Difference, d    (d - d)2
12    85    83    2    1
13    87    83    4    9
14    85    83    2    1
15    85    82    3    4
16    68    65    3    4
17    81    79    2    1
18    84    83    1    0
19    71    60    11    100
20    46    47    -1    4
21    75    77    -2    9
22    80    83    -3    16
Σ(d - d)2 = 270
d = 1

What is the 90% confidence interval for the mean difference between student scores on the math and English tests? Assume that the mean differences are approximately normally distributed.

1+1.3

That is the answer I am getting, but am not sure.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

#2 2013-03-22 02:13:23

bobbym
Administrator

Online

Re: Stats

Hi;

What does (d-d)2 mean?


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

#3 2013-03-22 02:19:49

ShivamS
Super Member

Online

Re: Stats

Since Σ(d - d)2 = 270, we get the sample mean difference.


I have discovered a truly marvellous signature, which this margin is too narrow to contain. -Fermat
Give me a lever long enough and a fulcrum on which to place it, and I shall move the world. -Archimedes
Young man, in mathematics you don't understand things. You just get used to them. - Neumann

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