Sampling Distribution of Difference between meansWatch

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Thread starter 14 years ago
#1
For my maths coursework, my teacher says to get high marks i must include

Sampling Distribution of Difference between means.

I've looked through it and its quite complicated. Can anyone make it a lot simpler for me please?
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14 years ago
#2
What data are you looking at?
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Thread starter 14 years ago
#3
the coursework is about newspapers and ive gotta inclue the number of words in a sentence and the number of letters in a word.
0
14 years ago
#4
Theory - you don't need data for this bit
Let X be the number of letters in a randomly selected word from The Independent. Let a and s^2 be the mean and variance of X.

Let Y be the number of letters in a randomly selected word from The Sun. Let b and t^2 be the mean and variance of Y.

Let Xbar be the average of n observations of X, and Ybar be the average of n observations of Y.

--

Then:

Xbar has mean a and variance s^2/n
Ybar has mean b and variance t^2/n
(Xbar - Ybar) has mean (a - b) and variance (s^2 + t^2)/n.

--

If a = b (ie, if the two newspapers have equally long words) then (Xbar - Ybar) has mean 0 and variance (s^2 + t^2)/n, and so

(Xbar - Ybar) / sqrt[(s^2 + t^2)/n] . . . . . (*)

has mean 0 and variance 1.

If, on the other hand, a > b (ie, if The Independent has longer words than The Sun) then (*) would tend to be larger.

--

Applying the theory to the data
Use your data to estimate s^2 and t^2. Then use those estimates to calculate an approximation to (*).

If the estimate is more than 2 then you can say: My estimate is more than two standard deviations above the mean. So there is strong evidence against the assumption that a = b. I conclude that The Independent has longer words than The Sun.

If the estimate is less than -2 then you can say: My estimate is more than two standard deviations below the mean. So there is strong evidence against the assumption that a = b. I conclude that The Independent has shorter words than The Sun.

Otherwise, if the estimate is between -2 and 2, then you can say: "My estimate is within two standard deviations of the mean. There is no strong evidence against the assumption that a = b. I conclude that the two newspapers have equally long words.
0
14 years ago
#5
THat might actually help me do it 0
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