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## #1 2013-03-21 02:51:50

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### 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.

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## #2 2013-03-21 03:13:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Stats

Hi;

What does (d-d)2 mean?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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## #3 2013-03-21 03:19:49

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Stats

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

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