- #1
Math_Frank
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Homework Statement
I am given the table
[tex]\begin{array}{ccccc} samplesite & 1950 & 1975 & Change \\ 1 & 7.30 & 7.70 & 0.40\\ 2 & 6.14 & 6.72 & 0.58 \\ 3 & 6.47 & 6.32 & -0.15 \\4 & 5.87 & 6.38 & 0.51 \\ 5 & 6.06 & 6.34 & 0.28 \\ 6 & 4.71 & 5.78 & 1.07 \\ 7 & 5.45 & 5.59 & 0.14 \\ 8 & 6.17 & 6.33 & 0.16 \\9 & 5.83 & 5.50 & -0.33 \\ 10 & 5.55 & 5.55 & 0.00 \\ 11 & 5.50 & 6.08 & 0.58 \end{array}[/tex]
I have to stachistics question where the above table is used.
Homework Statement
Question (1)
Look at the change column: Is the change in polution levels from 1950 to 1975 significant?
Using the significance test for unknown mean and unknown standard diviation.
So I use the formula:
[tex]t = \frac{\overline{x} - \mu_0}{\frac{s}{\sqrt{n}}}[/tex]
where [tex]\overline{x} = \frac{\sum(x_i)}{N} = \frac{3.24}{11} = 0.2946[/tex]
and where [tex]S^2 = \frac{1}{N-1} \sum(X -\overline{x})^2 = 0.154[/tex]
where S = [tex]\sqrt{S^2} = 0.394228[/tex]
Average change = average 1975 - average 1950. Under the null hypothesis, change = 0, then mu = 0
Then I insert into the formula
[tex]t = \frac{0.2946 - 0}{\frac{0.392428}{\sqrt{11}}} = 2.47813.[/tex]
Looking that up in the t-table Level of significans is 95%. How does that sound?
Homework Statement
Homework Equations
But what do I use for [tex]\mu_{0}[/tex] ??
Question (2):
Write the 95% confidence Interval for the mean and the variance for the change polution from 1950 og 1975.
The 95% confidence interval for the mean is defined
[tex]\overline{x} + t_{CL} \cdot {N} , \overline{x} - t_{CL} \cdot {N} [/tex]
I know that [tex]\overline{x} = 0.2945[/tex] and if look at the t table for 95% t-level at degree of freedom df = N - 1 then I find a t-value called t = 2.98.
Therefore (as I understand it) the 95% confidence level for the mean is
[tex]0.2945 + 2.95 \cdot {11} , 0.2945 - 2.98 \cdot {11} [/tex] ?
If the above is true how do I write the 95% Confidance Interval of the variance?
Sincerely Yours
Math Frank.
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