Respuesta :
I assume that says [tex]n=110[/tex] and [tex]\bar x = 98.0
[/tex] and [tex]\sigma = 0.74
[/tex].
It doesn't really tell us if this is the standard deviation of the individual samples or of the sample average. Since they're related by a factor of [tex] \sqrt{n} [/tex], around ten, some common sense tells us this is the standard deviation of the individual samples.
So we can conclude our sample mean has a standard deviation
[tex]s = \dfrac{ \sigma }{ \sqrt n } = \dfrac{.74}{ \sqrt{110}} = 0.0705562[/tex]
and that [tex]x=98.6[/tex] is
[tex]z = \dfrac{ x- \bar x}{s} = \dfrac{98.6 - 98.0}{0.0705562 } = 8.5[/tex]
That's a huge z score, 8.5 standard deviations away. 110 is big enough we can just use the normal distribution and not worry about t distributions.
We can conclude the 98.6 is very unlikely to be the true mean or close to the true mean of human temperatures.
It doesn't really tell us if this is the standard deviation of the individual samples or of the sample average. Since they're related by a factor of [tex] \sqrt{n} [/tex], around ten, some common sense tells us this is the standard deviation of the individual samples.
So we can conclude our sample mean has a standard deviation
[tex]s = \dfrac{ \sigma }{ \sqrt n } = \dfrac{.74}{ \sqrt{110}} = 0.0705562[/tex]
and that [tex]x=98.6[/tex] is
[tex]z = \dfrac{ x- \bar x}{s} = \dfrac{98.6 - 98.0}{0.0705562 } = 8.5[/tex]
That's a huge z score, 8.5 standard deviations away. 110 is big enough we can just use the normal distribution and not worry about t distributions.
We can conclude the 98.6 is very unlikely to be the true mean or close to the true mean of human temperatures.