What is the strongest statement that can be deduced about p?
$begingroup$
Let a test statistic $T$ be $t(3)$ distributed. Define $p = P(T ≥ 3)$.
What is the strongest statement that can be deduced about p?
If I'm correct, the strongest statement means that if you e.g. deduced that $p ≤ 0.50$, then $p ≤ 0.60$ is also true, but $p ≤ 0.50$ is a stronger statement, if you deduced that $p ≥ 0.50$, then $p ≥ 0.30$ is also true but $p ≥ 0.50$ is stronger, if you deduced that $0.30 ≤ p ≤ 0.50$ then $p ≤ 0.50$ is also true, but $0.30 ≤ p ≤ 0.50$ is stronger.
How can I compute the strongest statement for this test statistic? Thanks for the help!
Result: $0.025≤p≤0.05$
statistics
asked Jan 14 at 14:18
FTACFTAC
2719
$endgroup$
add a comment |
$begingroup$
Let a test statistic $T$ be $t(3)$ distributed. Define $p = P(T ≥ 3)$.
What is the strongest statement that can be deduced about p?
If I'm correct, the strongest statement means that if you e.g. deduced that $p ≤ 0.50$, then $p ≤ 0.60$ is also true, but $p ≤ 0.50$ is a stronger statement, if you deduced that $p ≥ 0.50$, then $p ≥ 0.30$ is also true but $p ≥ 0.50$ is stronger, if you deduced that $0.30 ≤ p ≤ 0.50$ then $p ≤ 0.50$ is also true, but $0.30 ≤ p ≤ 0.50$ is stronger.
How can I compute the strongest statement for this test statistic? Thanks for the help!
Result: $0.025≤p≤0.05$
statistics
asked Jan 14 at 14:18
FTACFTAC
2719
$endgroup$
2
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
1
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07
add a comment |
$begingroup$
Let a test statistic $T$ be $t(3)$ distributed. Define $p = P(T ≥ 3)$.
What is the strongest statement that can be deduced about p?
If I'm correct, the strongest statement means that if you e.g. deduced that $p ≤ 0.50$, then $p ≤ 0.60$ is also true, but $p ≤ 0.50$ is a stronger statement, if you deduced that $p ≥ 0.50$, then $p ≥ 0.30$ is also true but $p ≥ 0.50$ is stronger, if you deduced that $0.30 ≤ p ≤ 0.50$ then $p ≤ 0.50$ is also true, but $0.30 ≤ p ≤ 0.50$ is stronger.
How can I compute the strongest statement for this test statistic? Thanks for the help!
Result: $0.025≤p≤0.05$
statistics
asked Jan 14 at 14:18
FTACFTAC
2719
$endgroup$
Let a test statistic $T$ be $t(3)$ distributed. Define $p = P(T ≥ 3)$.
What is the strongest statement that can be deduced about p?
If I'm correct, the strongest statement means that if you e.g. deduced that $p ≤ 0.50$, then $p ≤ 0.60$ is also true, but $p ≤ 0.50$ is a stronger statement, if you deduced that $p ≥ 0.50$, then $p ≥ 0.30$ is also true but $p ≥ 0.50$ is stronger, if you deduced that $0.30 ≤ p ≤ 0.50$ then $p ≤ 0.50$ is also true, but $0.30 ≤ p ≤ 0.50$ is stronger.
How can I compute the strongest statement for this test statistic? Thanks for the help!
Result: $0.025≤p≤0.05$
statistics
statistics
asked Jan 14 at 14:18
FTACFTAC
2719
asked Jan 14 at 14:18
FTACFTAC
2719
asked Jan 14 at 14:18
FTACFTAC
2719
asked Jan 14 at 14:18
FTACFTAC
2719
asked Jan 14 at 14:18
FTACFTAC
2719
2719
2
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
1
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07
add a comment |
2
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
1
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07
2
2
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
1
1
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07
add a comment |
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2
$begingroup$
I don't understand. Is $tleft(3right)$ the Student t-distribution with 3 degrees of freedom? If so, why isn't $p$ a completely determined unique real number ($approx 0.0288$ , according to this calculator: surfstat.anu.edu.au/surfstat-home/tables/t.php)?
$endgroup$
– lonza leggiera
Jan 14 at 23:08
$begingroup$
I also don't know what they mean, maybe yes is a Student t-distribution but I'm not 100% sure
$endgroup$
– FTAC
Jan 15 at 7:48
1
$begingroup$
What I don't understand is what the question "What is the strongest statement that can be deduced about p?" is asking for. If $T$ is distributed as a Student t with 3 degrees of freedom, then $p = int_3^infty fleft(tright) dt = 1 - int_{-infty}^3 fleft(tright) dt$ , where $f$ is the probabilty density function of that distribution, so $p$ would be a uniquely defined real number to which you can find arbitrarily close rational approximations. The question "what's the strongest statement you can deduce about $p$ ?" seems to me to be too vague to make any sense.
$endgroup$
– lonza leggiera
Jan 15 at 9:07