Sample size and margin of error in a confidence interval for a mean
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I am having trouble understanding this problem:
Darren wants to estimate the mean age in a population of trees. He'll sample $n$ trees and build a $90%$ confidence interval for the mean age. He doesn't want the margin of error to exceed $3$ years. Preliminary data suggests that the standard deviation for the ages of trees in this population is $sigma=16$ years.
Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Choice A: 7 $$$$ Choice B: 20 $$$$ Choice C: 30 $$$$ Choice D: 44 $$$$ Choice E: 77 $$$$
This is what I did: Looked at a z table and found $90%$ $CI$ corresponds to $approx1.283%$. Then I solved the following inequality:
$$z^*cdotfrac{sigma}{sqrt{n}}leq3$$ $$sigma=16quad zapprox1.283$$
I ended up getting about $46$ trees because of the rounding for the critical $z$ value. So I chose answer for $44$ trees. The correct answer says to use the critical $z$ value of $1.645$ but this places the $CI$ at $95%$. Why is $1.645$ used?
statistics confidence-interval
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
$endgroup$
add a comment |
$begingroup$
I am having trouble understanding this problem:
Darren wants to estimate the mean age in a population of trees. He'll sample $n$ trees and build a $90%$ confidence interval for the mean age. He doesn't want the margin of error to exceed $3$ years. Preliminary data suggests that the standard deviation for the ages of trees in this population is $sigma=16$ years.
Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Choice A: 7 $$$$ Choice B: 20 $$$$ Choice C: 30 $$$$ Choice D: 44 $$$$ Choice E: 77 $$$$
This is what I did: Looked at a z table and found $90%$ $CI$ corresponds to $approx1.283%$. Then I solved the following inequality:
$$z^*cdotfrac{sigma}{sqrt{n}}leq3$$ $$sigma=16quad zapprox1.283$$
I ended up getting about $46$ trees because of the rounding for the critical $z$ value. So I chose answer for $44$ trees. The correct answer says to use the critical $z$ value of $1.645$ but this places the $CI$ at $95%$. Why is $1.645$ used?
statistics confidence-interval
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
$endgroup$
add a comment |
$begingroup$
I am having trouble understanding this problem:
Darren wants to estimate the mean age in a population of trees. He'll sample $n$ trees and build a $90%$ confidence interval for the mean age. He doesn't want the margin of error to exceed $3$ years. Preliminary data suggests that the standard deviation for the ages of trees in this population is $sigma=16$ years.
Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Choice A: 7 $$$$ Choice B: 20 $$$$ Choice C: 30 $$$$ Choice D: 44 $$$$ Choice E: 77 $$$$
This is what I did: Looked at a z table and found $90%$ $CI$ corresponds to $approx1.283%$. Then I solved the following inequality:
$$z^*cdotfrac{sigma}{sqrt{n}}leq3$$ $$sigma=16quad zapprox1.283$$
I ended up getting about $46$ trees because of the rounding for the critical $z$ value. So I chose answer for $44$ trees. The correct answer says to use the critical $z$ value of $1.645$ but this places the $CI$ at $95%$. Why is $1.645$ used?
statistics confidence-interval
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
$endgroup$
I am having trouble understanding this problem:
Darren wants to estimate the mean age in a population of trees. He'll sample $n$ trees and build a $90%$ confidence interval for the mean age. He doesn't want the margin of error to exceed $3$ years. Preliminary data suggests that the standard deviation for the ages of trees in this population is $sigma=16$ years.
Which of these is the smallest approximate sample size required to obtain the desired margin of error?
Choice A: 7 $$$$ Choice B: 20 $$$$ Choice C: 30 $$$$ Choice D: 44 $$$$ Choice E: 77 $$$$
This is what I did: Looked at a z table and found $90%$ $CI$ corresponds to $approx1.283%$. Then I solved the following inequality:
$$z^*cdotfrac{sigma}{sqrt{n}}leq3$$ $$sigma=16quad zapprox1.283$$
I ended up getting about $46$ trees because of the rounding for the critical $z$ value. So I chose answer for $44$ trees. The correct answer says to use the critical $z$ value of $1.645$ but this places the $CI$ at $95%$. Why is $1.645$ used?
statistics confidence-interval
statistics confidence-interval
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
asked Dec 12 '18 at 16:47
JinzuJinzu
381413
381413
add a comment |
add a comment |
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