Std Deviation of a point estimate which is the sum of two normally and independently distributed random...
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The problem States:
Given $bar x= 41$ and $bar y= 40.7$.
$σ_x= 0.1$ and $σ_y= 0.19$
$X sim N[mu_X; sigma^2]; Y sim N[mu_Y ; sigma^2]$; with $mu_X > 0,; mu_Y > 0, sigma > 0$ and $theta = µ_X - µ_Y$ .
The two samples are independently distributed and have $n_X = n_Y = 18$.
Now it asks me to find the point estimate for $theta$ and its standard deviation.
The point estimate is simply $hat{θ} = bar x − bar y = 41 − 40.7 = 0.3$
Now I have no idea how to find the standard deviation..can't find any similar example on my book or on google.
The solution I'm given is: Standard deviation = $0.05$
https://i.stack.imgur.com/xiOz4.png
statistics statistical-inference parameter-estimation
edited Jan 6 at 15:27
Sauhard Sharma
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
$endgroup$
add a comment |
$begingroup$
The problem States:
Given $bar x= 41$ and $bar y= 40.7$.
$σ_x= 0.1$ and $σ_y= 0.19$
$X sim N[mu_X; sigma^2]; Y sim N[mu_Y ; sigma^2]$; with $mu_X > 0,; mu_Y > 0, sigma > 0$ and $theta = µ_X - µ_Y$ .
The two samples are independently distributed and have $n_X = n_Y = 18$.
Now it asks me to find the point estimate for $theta$ and its standard deviation.
The point estimate is simply $hat{θ} = bar x − bar y = 41 − 40.7 = 0.3$
Now I have no idea how to find the standard deviation..can't find any similar example on my book or on google.
The solution I'm given is: Standard deviation = $0.05$
https://i.stack.imgur.com/xiOz4.png
statistics statistical-inference parameter-estimation
edited Jan 6 at 15:27
Sauhard Sharma
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
$endgroup$
$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31
add a comment |
$begingroup$
The problem States:
Given $bar x= 41$ and $bar y= 40.7$.
$σ_x= 0.1$ and $σ_y= 0.19$
$X sim N[mu_X; sigma^2]; Y sim N[mu_Y ; sigma^2]$; with $mu_X > 0,; mu_Y > 0, sigma > 0$ and $theta = µ_X - µ_Y$ .
The two samples are independently distributed and have $n_X = n_Y = 18$.
Now it asks me to find the point estimate for $theta$ and its standard deviation.
The point estimate is simply $hat{θ} = bar x − bar y = 41 − 40.7 = 0.3$
Now I have no idea how to find the standard deviation..can't find any similar example on my book or on google.
The solution I'm given is: Standard deviation = $0.05$
https://i.stack.imgur.com/xiOz4.png
statistics statistical-inference parameter-estimation
edited Jan 6 at 15:27
Sauhard Sharma
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
$endgroup$
The problem States:
Given $bar x= 41$ and $bar y= 40.7$.
$σ_x= 0.1$ and $σ_y= 0.19$
$X sim N[mu_X; sigma^2]; Y sim N[mu_Y ; sigma^2]$; with $mu_X > 0,; mu_Y > 0, sigma > 0$ and $theta = µ_X - µ_Y$ .
The two samples are independently distributed and have $n_X = n_Y = 18$.
Now it asks me to find the point estimate for $theta$ and its standard deviation.
The point estimate is simply $hat{θ} = bar x − bar y = 41 − 40.7 = 0.3$
Now I have no idea how to find the standard deviation..can't find any similar example on my book or on google.
The solution I'm given is: Standard deviation = $0.05$
https://i.stack.imgur.com/xiOz4.png
statistics statistical-inference parameter-estimation
statistics statistical-inference parameter-estimation
edited Jan 6 at 15:27
Sauhard Sharma
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
edited Jan 6 at 15:27
Sauhard Sharma
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
edited Jan 6 at 15:27
Sauhard Sharma
953318
edited Jan 6 at 15:27
Sauhard Sharma
953318
edited Jan 6 at 15:27
Sauhard Sharma
953318
953318
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
asked Jan 6 at 13:49
TroubledEconomistTroubledEconomist
12
12
$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31
add a comment |
$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31
$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31
add a comment |
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$begingroup$
How have you calculated the point estimate ?
$endgroup$
– Sauhard Sharma
Jan 6 at 14:11
$begingroup$
I got lost in the formatting and forgot to specify some important data in my question, it should be clearer now, sorry for the inconvenience
$endgroup$
– TroubledEconomist
Jan 6 at 14:59
$begingroup$
a google search "variance difference of sample means" gives the very first hit kean.edu/~fosborne/bstat/05b2means.html
$endgroup$
– Just_to_Answer
Jan 7 at 6:31