Respuesta :
The relationship between the two confidence intervals is that"The width of I81 will be 1/3 the width of I9." Option B
What is the relationship between the two confidence intervals?
Question Parameters:
Two 99 percent confidence intervals
One confidence interval, i9
the other confidence interval, i81,
samples of size 81 from each of r and w.
Let
Confidence level=0.05
standard deviation [tex]\sigma=6[/tex]
Generally, the equation for the confidence interval is mathematically given as
[tex]CI=(\frac{z_{0.05}*\sigma}{2*\sqrt{n}} )[/tex]
For i9
CI=(1.96*6}{\sqrt{9}} )
Cl=3.92
For i81
CI'=(1.96*6}{\sqrt{81}})
Cl'=1.3067
In conclusion the relationship between confidence interval, i9 and confidence interval, i81
i81=1/3i9
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Complete Question
Two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, R and W. One confidence interval, 19, will be constructed using samples of size 9 from each of R and W. and the other confidence interval, Ist, will be constructed using samples of size 81 from each of R and W. When all other things remain the same, which of the following describes the relationship between the two confidence intervals?
A width of 181 will be the width of I9.
B The width of I81 will be 1/3 the width of I9.
C The width of 181 will be equal to the width of I9.
DThe width of 191 will be 3 times the width of I9.
EThe width of 181 will be 9 times the width of I9.
