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Sagot :
Answer:
The length of the interval is of 1.8672.
Step-by-step explanation:
Length of a confidence interval:
Margin of error multiplied by 2.
Confidence interval:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
s=8.57, n=300
[tex]\sigma = 8.25, n = 300[/tex]
Margin of error:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{8.25}{\sqrt{300}}[/tex]
[tex]M = 0.9336[/tex]
Length:
2*0.9336 = 1.8672
The length of the interval is of 1.8672.
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