Std Deviation of a point estimate which is the sum of two normally and independently distributed random...












0












$begingroup$


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










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$endgroup$












  • $begingroup$
    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
















0












$begingroup$


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










share|cite|improve this question











$endgroup$












  • $begingroup$
    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














0












0








0





$begingroup$


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










share|cite|improve this question











$endgroup$




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






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 6 at 15:27









Sauhard Sharma

913318




913318










asked Jan 6 at 13:49









TroubledEconomistTroubledEconomist

11




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










  • $begingroup$
    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










  • $begingroup$
    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










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