Question

Stout - STAI 130-900C - Fall 19. WU > Activities and Due Dates > HW-(16) Assignment Score: 500/1000 Resources C Give Up? Check Answer Question 10 of 10 > An NHANES report gives data for 652 women aged 20-29 years. The BMI of these 662 women was -26.6. On the Student Assignment Container basis of this sample, we want to estimate the BMI w in the population of all 20.6 million women in this age groc treated these data as an SRS from a Normally distributed population with standard deviation - 7.2. (a) Give three confidence intervals for the mean BMI in this population, using 90%,95%, and 99% confidence. Enter the lower and upper bound for the 90% confidence interval. (Enter your answers rounded to two decimal places. If you are using Crunchlt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.) lower bound upper bound Question Source: Moore, The Basic Practice of Statistics, le Publisher W.H. Freemar 1:39 PM 11/23/2019

Answer 1

Solution

652, x = 26.5, o =7.2 given : n

formula Confidence interval for the population mean,

Margin of (E) (E) Where, Margin of error error Vn

download for excel to find Z

https://drive.google.com/open?id=1miDykB956rSHGgAYD93YaJKxmD9a_oZ1

$\mathbf{Confidence\;level:}$	$\mathbf{z_{\frac{\alpha }{2}}}$
$\mathbf{90\%}$	${\color{Blue} \mathbf{1.645}}$
95	${\color{Blue} \mathbf{1.960}}$
$\mathbf{99\%}$	${\color{Blue} \mathbf{2.576}}$

${\color{Blue} \mathbf{(a)}}\;{\color{magenta} \mathbf{for\;90\%\;confidence\;interval:}}$

$=26.5 \pm 1.645*\left \{ \frac{7.2}{\sqrt{652}} \right \}$

$=26.5 \pm 0.46$

$\mathbf{lower\;bound}=26.5 - 0.46=\mathbf{{\color{Red} 26.04}}$

$\mathbf{upper\;bound}=26.5+0.46=\mathbf{{\color{Red} 26.96}}$

${\color{Magenta} \mathbf{for\;95\%\;confidence\;interval:}}$

$=26.5 \pm 1.960*\left \{ \frac{7.2}{\sqrt{652}} \right \}$

$=26.5 \pm 0.55$

$\mathbf{lower\;bound}=26.5 - 0.55=\mathbf{{\color{Red} 25.95}}$

$\mathbf{upper\;bound}=26.5+0.55=\mathbf{{\color{Red} 27.05}}$

${\color{Magenta} \mathbf{for\;99\%\;confidence\;interval:}}$

$=26.5 \pm 2.576*\left \{ \frac{7.2}{\sqrt{652}} \right \}$

$=26.5 \pm 0.73$

$\mathbf{lower\;bound}=26.5 - 0.73=\mathbf{{\color{Red} 25.77}}$

$\mathbf{upper\;bound}=26.5+0.73=\mathbf{{\color{Red} 27.23}}$

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${\color{Blue} \mathbf{(b)}}\;$

${\color{Magenta} \mathbf{margin\;of\;error\;for\;a\;90\% \;confidence \;interval}}=\mathbf{{\color{Red}0.46 }}$

${\color{Magenta} \mathbf{margin\;of\;error\;for\;a\;95\% \;confidence \;interval}}=\mathbf{{\color{Red}0.55 }}$

${\color{Magenta} \mathbf{margin\;of\;error\;for\;a\;99\% \;confidence \;interval}}=\mathbf{{\color{Red}0.73}}$

${\color{Red} \mathbf{The\; margin\;of\;error\; increases\; as\; the\;confidence\; level \;increases.}}$